Datasets:

mponty

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code_champs_solutions

like 2

s973607152

p04051

cpp

Accepted

#include <bits/stdc++.h> // iostream is too mainstream #include <cstdio> // bitch please #include <iostream> #include <algorithm> #include <cstdlib> #include <vector> #include <set> #include <map> #include <queue> #include <stack> #include <list> #include <cmath> #include <iomanip> #include <time.h> #define dibs reserve #define OVER9000 1234567890 #define ALL_THE(CAKE,LIE) for(auto LIE =CAKE.begin(); LIE != CAKE.end(); LIE++) #define tisic 47 #define soclose 1e-8 #define chocolate win // so much chocolate #define patkan 9 #define ff first #define ss second #define abs(x) ((x < 0)?-(x):x) #define uint unsigned int #define dbl long double #define pi 3.14159265358979323846 using namespace std; // mylittledoge #ifdef DONLINE_JUDGE // palindromic tree is better than splay tree! #define lld I64d #endif long long mod =1000000007; long long pw(long long a, long long e) { if(e <= 0) return 1; long long x =pw(a,e/2); x =(x*x)%mod; if(e%2 != 0) x =(x*a)%mod; return x;} int main() { cin.sync_with_stdio(0); cin.tie(0); cout << fixed << setprecision(10); int N; cin >> N; vector<long long> fac(10000,1),inv(10000,1); for(int i =1; i < 10000; i++) { fac[i] =(i*fac[i-1])%mod; inv[i] =pw(fac[i],mod-2);} vector< vector<long long> > P(2048,vector<long long>(2048,0)); for(int i =0; i < N; i++) { int a,b; cin >> a >> b; P[a][b]++;} vector< vector<long long> > P0 =P; for(int i =2000; i > 0; i--) for(int j =2000; j > 0; j--) { P[i][j-1] +=P[i][j]; if(P[i][j-1] >= mod) P[i][j-1] -=mod; P[i-1][j] +=P[i][j]; if(P[i-1][j] >= mod) P[i-1][j] -=mod; P[i][j] =0;} long long ans =0; for(int i =2000; i >= -2000; i--) for(int j =2000; j >= -2000; j--) { int x1 =max(i,0), y1 =max(-i,0); int x2 =max(j,0), y2 =max(-j,0); long long x =(fac[x1+x2+y1+y2]*inv[x1+x2])%mod; x =(x*inv[y1+y2])%mod; long long p =(P[x1][y1]*P[x2][y2])%mod; ans =(ans+p*x)%mod;} for(int i =0; i < 2048; i++) for(int j =0; j < 2048; j++) { long long x =(fac[2*(i+j)]*inv[2*i])%mod; x =(x*inv[2*j])%mod; ans =(ans-P0[i][j]%mod*x)%mod;} ans =(ans*inv[2])%mod; if(ans < 0) ans +=mod; cout << ans << "\n"; return 0;} // look at my code // my code is amazing

codenet

s083138940

p04051

cpp

Accepted

#include <string> #include <vector> #include <algorithm> #include <numeric> #include <set> #include <map> #include <queue> #include <iostream> #include <sstream> #include <cstdio> #include <cmath> #include <ctime> #include <cstring> #include <cctype> #include <cassert> #include <limits> #include <functional> #include <iomanip> #include <complex> #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) #if defined(_MSC_VER) || __cplusplus > 199711L #define aut(r,v) auto r = (v) #else #define aut(r,v) __typeof(v) r = (v) #endif #define each(it,o) for(aut(it, (o).begin()); it != (o).end(); ++ it) #define all(o) (o).begin(), (o).end() #define pb(x) push_back(x) #define mp(x,y) make_pair((x),(y)) #define mset(m,v) memset(m,v,sizeof(m)) #define INF 0x3f3f3f3f #define INFL 0x3f3f3f3f3f3f3f3fLL using namespace std; typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll; typedef pair<pii,int> ppiii ; template<typename T, typename U> inline void amin(T &x, U y) { if(y < x) x = y; } template<typename T, typename U> inline void amax(T &x, U y) { if(x < y) x = y; } typedef complex<double> P; ll MOD = 1e9 + 7; int n,m,Q; ll dp[4010][4010]={0}; ll fact[202020], frev[202020];//階乗,逆元 ll C(int p, int q) { if (q < 0 || p < q) return 0; return fact[p] * frev[q] % MOD * frev[p - q] % MOD; } ll modpow(ll a, ll b) {//a^b%mod ll res = 1; for (; b > 0; a = a * a % MOD, b /= 2) if (b & 1) res = res * a % MOD; return res; } int main(){ cin>>n; int a,b; vector<pii> data(n); fact[0] = frev[0] = 1; for (int i = 1; i <= 10000; ++i) { fact[i] = (fact[i - 1] * i) % MOD; frev[i] = modpow(fact[i],MOD-2); } for(int i=0;i<n;i++){ cin>>a>>b; dp[2001-a][2001-b]++; data[i]=mp(a,b); } for(int i=1;i<=4009;i++){ for(int j=1;j<=4009;j++){ dp[i][j]=(dp[i][j]+dp[i-1][j]+dp[i][j-1])%MOD; } } //cout<<dp[0][9]<<endl; ll ans=0; for(int i=0;i<n;i++){ int p=data[i].first,q=data[i].second; ans=(ans+dp[2001+p][2001+q])%MOD; ans=(ans+MOD-C(2*p+2*q,2*q))%MOD; } ans=(ans*frev[2])%MOD; cout<<ans<<endl; }

codenet

s969485256

p04051

cpp

Accepted

#include <iostream> #include <cstdio> #include <vector> #include <string> #include <algorithm> #define rep(i,n) for(int i=0; i<(n); i++) #define rrep(i,n) for(int i=(n)-1; i>=0; i--) #define all(X) (X).begin(),(X).end() using namespace std; typedef long long int ll; typedef pair<int,int> P; template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; } template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; } template<class A, size_t N, class T> void Fill(A (&a)[N], const T &v){ fill( (T*)a, (T*)(a+N), v ); } const int INF = 0x3fffffff; //const int MOD = 10e9+7; const int MOD = 1000000007; // n^m%MOD を求める。O( log(m) ) ll modpow(ll n, int m){ ll ret=1; for(int i=1; i<=m; i<<=1, (n*=n)%=MOD){ if( m&i ) (ret *= n) %= MOD; } return ret; } // 逆元を求める ll modinv(ll n){ return modpow( n, MOD-2 ); } // 階乗を求める。O(1) 準備O( n*log(n) ) // fact[n] : nの階乗 // fact.inv[n] : nの階乗の逆元 class FACTORIAL{ public: const int MAX_NUM = 10004; // 最大のn vector<ll> fact; vector<ll> inv; FACTORIAL(): fact(MAX_NUM), inv(MAX_NUM) { fact[0] = 1; for(ll i=1; i<MAX_NUM; i++){ fact[i] = (fact[i-1] * i) % MOD; inv[i] = modpow( fact[i], MOD-2 ); } } const ll& operator [ ] ( const int i ) const { return fact[i]; } } fact; // 組み合わせ(Combinationを求める) O(1) ll cmb(unsigned int n, unsigned int r){ if( n < r ) return 0; return fact[n] * fact.inv[r] % MOD * fact.inv[n-r] % MOD; } ll f(ll a, ll b){ return cmb( a+b, a ); } ll dp[4050][4050]; int main(){ ll N, A[200005], B[200005], ans=0; int offset = 2005; cin >> N; rep(i,N){ cin >> A[i] >> B[i]; dp[ offset-A[i] ][ offset-B[i] ] += 1; } rep(i,4010) rep(j,4010){ dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % MOD; dp[i][j+1] = (dp[i][j+1] + dp[i][j]) % MOD; } ll sum = 0; rep(i,N){ sum = (sum + dp[ offset+A[i] ][ offset+B[i] ]) % MOD; } // cout << sum << endl; // ll sum2 = 0; // rep(i,N) rep(j,N){ // sum2 = (sum2 + f(A[i]+A[j], B[i]+B[j]) ) % MOD; // } // cout << sum2 << endl; ll db = 0; // ダブリ rep(i,N){ db = (db + f( A[i]+A[i], B[i]+B[i] ) ) % MOD; } ans = (((sum + MOD - db) % MOD) * modinv(2) ) % MOD; cout << ans << endl; return 0; }

codenet

s836551848

p04051

cpp

Accepted

#include <iostream> #include <stdio.h> #include <math.h> #include <string.h> #include <time.h> #include <stdlib.h> #include <string> #include <bitset> #include <vector> #include <set> #include <map> #include <queue> #include <algorithm> #include <sstream> #include <stack> #include <iomanip> using namespace std; #define pb push_back #define mp make_pair typedef pair<int,int> pii; typedef long long ll; typedef double ld; typedef vector<int> vi; #define fi first #define se second #define fe first #define FO(x) {freopen(#x".in","r",stdin);freopen(#x".out","w",stdout);} #define Edg int M=0,fst[SZ],vb[SZ],nxt[SZ];void ad_de(int a,int b){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;}void adde(int a,int b){ad_de(a,b);ad_de(b,a);} #define Edgc int M=0,fst[SZ],vb[SZ],nxt[SZ],vc[SZ];void ad_de(int a,int b,int c){++M;nxt[M]=fst[a];fst[a]=M;vb[M]=b;vc[M]=c;}void adde(int a,int b,int c){ad_de(a,b,c);ad_de(b,a,c);} #define es(x,e) (int e=fst[x];e;e=nxt[e]) #define esb(x,e,b) (int e=fst[x],b=vb[e];e;e=nxt[e],b=vb[e]) #define VIZ {printf("digraph G{\n"); for(int i=1;i<=n;i++) for es(i,e) printf("%d->%d;\n",i,vb[e]); puts("}");} #define VIZ2 {printf("graph G{\n"); for(int i=1;i<=n;i++) for es(i,e) if(vb[e]>=i)printf("%d--%d;\n",i,vb[e]); puts("}");} #define SZ 666666 const int MOD=1e9+7; ll fac[SZ],rfac[SZ]; ll qp(ll a,ll b) { ll x=1; a%=MOD; while(b) { if(b&1) x=x*a%MOD; a=a*a%MOD; b>>=1; } return x; } ll cnt[4005][4005]; int n,a[SZ],b[SZ]; int main() { fac[0]=1; for(int i=1;i<SZ;++i) fac[i]=fac[i-1]*i%MOD; rfac[SZ-1]=qp(fac[SZ-1],MOD-2); for(int i=SZ-1;i>=1;--i) rfac[i-1]=rfac[i]*i%MOD; scanf("%d",&n); for(int i=1;i<=n;++i) { scanf("%d%d",a+i,b+i); ++cnt[2001-a[i]][2001-b[i]]; } for(int i=1;i<=4002;++i) for(int j=1;j<=4002;++j) { cnt[i][j]+=cnt[i][j-1]+cnt[i-1][j]; (cnt[i][j]>=MOD)?(cnt[i][j]-=MOD):0; (cnt[i][j]>=MOD)?(cnt[i][j]-=MOD):0; (cnt[i][j]>=MOD)?(cnt[i][j]-=MOD):0; } ll ans=0,t=0; for(int i=1;i<=n;++i) { (ans+=cnt[2001+a[i]][2001+b[i]])%=MOD; t+=fac[a[i]+a[i]+b[i]+b[i]] *rfac[a[i]+a[i]]%MOD*rfac[b[i]+b[i]]%MOD; } const ll i2=(MOD+1)/2; t%=MOD; (ans-=t)%=MOD; ans=ans*i2%MOD; ans=(ans%MOD+MOD)%MOD; printf("%d\n",int(ans)); }

codenet

s523911942

p04051

cpp

Accepted

#include"bits/stdc++.h" #define PB push_back #define PF push_front #define LB lower_bound #define UB upper_bound #define fr(x) freopen(x,"r",stdin) #define fw(x) freopen(x,"w",stdout) #define iout(x) printf("%d\n",x) #define lout(x) printf("%lld\n",x) #define REP(x,l,u) for(int x = (l);x<=(u);x++) #define RREP(x,l,u) for(int x = (l);x>=(u);x--) #define mst(x,a) memset(x,a,sizeof(x)) #define PII pair<int,int> #define PLL pair<ll,ll> #define MP make_pair #define se second #define fi first #define dbg(x) cout<<#x<<" = "<<(x)<<endl; #define sz(x) ((int)x.size()) #define cl(x) x.clear() typedef long long ll; typedef unsigned long long ull; typedef double db; typedef long double ld; using namespace std; const int maxn = 200010; const int mod = 1e9+7,bas = 2500; const int MAX = 1000000010; const double eps = 1e-6; const double PI = acos(-1); template<typename T> inline void read(T &x){ x=0;T f=1;char ch;do{ch=getchar();if(ch=='-')f=-1;}while(ch<'0'||ch>'9');do x=x*10+ch-'0',ch=getchar();while(ch<='9'&&ch>='0');x*=f; } template<typename A,typename B> inline void read(A&x,B&y){read(x);read(y);} template<typename A,typename B,typename C> inline void read(A&x,B&y,C&z){read(x);read(y);read(z);} template<typename A,typename B,typename C,typename D> inline void read(A&x,B&y,C&z,D&w){read(x);read(y);read(z);read(w);} template<typename A,typename B> inline A fexp(A x,B p){A ans=1;for(;p;p>>=1,x=1LL*x*x%mod)if(p&1)ans=1LL*ans*x%mod;return ans;} template<typename A,typename B> inline A fexp(A x,B p,A mo){A ans=1;for(;p;p>>=1,x=1LL*x*x%mo)if(p&1)ans=1LL*ans*x%mo;return ans;} int n; int A[maxn],B[maxn]; int dp[5010][5010]; int fac[8010],inv[8010]; void Work(){ REP(i,-2000,2000) REP(j,-2000,2000)dp[i+bas][j+bas]=(dp[i-1+bas][j+bas]+dp[i+bas][j-1+bas]+dp[i+bas][j+bas])%mod; int ans=0; REP(i,1,n)ans=(ans+dp[A[i]+bas][B[i]+bas])%mod; REP(i,1,n)ans=(ans-1ll*fac[A[i]+A[i]+B[i]+B[i]]*inv[A[i]+A[i]]%mod*inv[B[i]+B[i]]%mod+mod)%mod; ans=1ll*ans*fexp(2,mod-2)%mod; iout(ans); } void Init(){ read(n); REP(i,1,n)read(A[i],B[i]),dp[bas-A[i]][bas-B[i]]++; fac[0]=1;REP(i,1,8000)fac[i]=1ll*fac[i-1]*i%mod; REP(i,0,8000)inv[i]=fexp(fac[i],mod-2); } int main(){ Init(); Work(); return 0; }

codenet

s402706464

p04051

cpp

Accepted

#include <bits/stdc++.h> #define loop(i,n) for(int i = 0;i < (n);i++) #define range(i,a,b) for(int i = (a);i <= (b);i++) #define all(A) A.begin(),A.end() #define pb push_back #define mp make_pair #define sz(A) ((int)A.size()) #define vi vector<int> #define vl vector<long long> #define vd vector<double> #define vp vector<pair<int,int> > #define ll long long #define pi pair<int,int> #define popcnt(x) __builtin_popcountll(x) #define LSOne(x) ((x) & (-(x))) #define xx first #define yy second #define PQ priority_queue #define print(A,t) cerr << #A << ": "; copy(all(A),ostream_iterator<t>(cerr," " )); cerr << endl #define prp(p) cerr << "(" << (p).first << " ," << (p).second << ")"; #define prArr(A,n,t) cerr << #A << ": "; copy(A,A + n,ostream_iterator<t>(cerr," " )); cerr << endl #define PRESTDIO() cin.tie(0),cerr.tie(0),ios_base::sync_with_stdio(0) #define what_is(x) cerr << #x << " is " << x << endl #define bit_lg(x) (assert(x > 0),__builtin_ffsll(x) - 1) const double PI = acos(-1); using namespace std; const int MAX = 200*1000 + 10,MAXA = 2*2000 + 10,MAXB = 2*MAXA,mod = 1e9 + 7; int A[MAX],B[MAX],n; int cnt[MAXA][MAXA],f[MAXA][MAXA]; int fact[MAXB],inv[MAXB]; int add(int a,int b){ a += b; if(a >= mod) a -= mod; if(a < 0) a += mod; return a; } int mul(int a,int b){ return (a*1LL*b)%mod; } int pow_mod(int a,int b){ if(!b) return 1; int x = 1; for(;b > 1;b >>= 1){ if(b & 1) x = mul(a,x); a = mul(a,a); } return mul(a,x); } void init(){ fact[0] = 1; loop(i,MAXB-1) fact[i + 1] = mul(fact[i],i + 1); loop(i,MAXB) inv[i] = pow_mod(fact[i],mod-2); } int C(int n,int k){ if(n < k) return 0; return mul(fact[n],mul(inv[k],inv[n - k])); } int main(){ #ifdef HOME freopen("in.in", "r", stdin); #endif init(); scanf("%d",&n); loop(i,n) { scanf("%d %d",A + i,B + i); cnt[2000-A[i]][2000-B[i]]++; } for(int x = 0;x <= 4000;x++) for(int y = 0;y <= 4000;y++) { f[x][y] = cnt[x][y]; if(x) f[x][y] = add(f[x][y],f[x - 1][y]); if(y) f[x][y] = add(f[x][y],f[x][y - 1]); } int ans = 0; loop(i,n){ int x = A[i],y = B[i]; ans = add(ans,f[x + 2000][y + 2000]); ans = add(ans,-C(2*x + 2*y,2*y)); } ans = (ans * 500000004LL)%mod; cout << ans << endl; return 0; }

codenet

s233643637

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; const int64_t MOD = 1e9+7; void add(int64_t& a, int64_t b){ a = (a+b) % MOD; } void mul(int64_t& a, int64_t b){ a = a*b % MOD; } vector<int64_t> fact, seq_inv, fact_inv; void create_fact_mod(int num){ fact[0] = fact[1] = 1; for(int i=2; i<=num; i++) fact[i] = fact[i-1] * i % MOD; } void create_seq_inv_mod(int num){ seq_inv[0] = seq_inv[1] = 1; for(int i=2; i<=num; i++) seq_inv[i] = (MOD - MOD/i) * seq_inv[MOD%i] % MOD; } void create_fact_inv_mod(int num){ fact_inv[0] = fact_inv[1] = 1; for(int i=2; i<=num; i++) fact_inv[i] = fact_inv[i-1] * seq_inv[i] % MOD; } void create_mod_tables(int num){ fact.resize(num+1); seq_inv.resize(num+1); fact_inv.resize(num+1); create_fact_mod(num); create_seq_inv_mod(num); create_fact_inv_mod(num); } int64_t comb_mod(int n, int k){ return fact[n] * fact_inv[n-k] % MOD * fact_inv[k] % MOD; } int64_t perm_mod(int n, int k){ return fact[n] * fact_inv[n-k] % MOD; } int64_t power_mod(int64_t num, int64_t power){ int64_t prod = 1; num %= MOD; while(power > 0){ if(power&1) prod = prod * num % MOD; num = num * num % MOD; power >>= 1; } return prod; } int64_t extgcd(int64_t a, int64_t b, int64_t& x, int64_t& y){ int64_t d = a; if(b != 0){ d = extgcd(b, a%b, y, x); y -= (a/b) * x; }else{ x = 1; y = 0; } return d; } int64_t inv_mod(int64_t a){ int64_t x, y; extgcd(a, MOD, x, y); return (MOD + x%MOD) % MOD; } int main(){ int N; cin >> N; vector<int> A(N), B(N); static int in[4001][4001], out[4001][4001]; for(int i=0; i<N; i++){ cin >> A[i] >> B[i]; in[2000-A[i]][2000-B[i]]++; out[2000+A[i]][2000+B[i]]++; } static int64_t dp[4001][4001]; int64_t ans = 0; for(int i=0; i<=4000; i++) for(int j=0; j<=4000; j++){ dp[i][j] = in[i][j]; if(i) add(dp[i][j], dp[i-1][j]); if(j) add(dp[i][j], dp[i][j-1]); add(ans, dp[i][j] * out[i][j]); } create_mod_tables(8000); for(int i=0; i<N; i++) add(ans, MOD - comb_mod(2*A[i]+2*B[i], 2*A[i])); mul(ans, inv_mod(2)); cout << ans << endl; }

codenet

s294263837

p04051

cpp

Accepted

#include <set> #include <map> #include <cmath> #include <ctime> #include <bitset> #include <string> #include <vector> #include <cstdio> #include <cstdlib> #include <cstring> #include <cassert> #include <iomanip> #include <iostream> #include <algorithm> #define PR pair #define fi first #define se second #define mk make_pair #define pb push_back #define REP(i, x, y) for(int i = (int)(x); i <= (int)(y); i++) #define FOR(i, x, y) for(int i = (int)(x); i < (int)(y); i++) #define PER(i ,x, y) for(int i = (int)(x); i >= (int)(y); i--) #define CH ch = getchar() #define Exit(...) printf(__VA_ARGS__), exit(0) #define dln() fprintf(stderr,"\n") #define dprintf(...) fprintf(stderr,__VA_ARGS__) using namespace std; typedef double db; typedef long long LL; typedef vector<int> VI; typedef vector<VI > VII; typedef PR<int,int> PII; typedef vector<PII> VPI; const int inf=2e9; const LL Inf=1e10; const int P=1e9+7; const int N=200005; inline LL IN(){ LL x = 0; int ch = 0, f = 0; for (CH; ch != -1 && (ch < 48 || ch > 57); CH) f = (ch == '-'); for (; ch >= 48 && ch <= 57; CH) x = (x << 1) + (x << 3) + ch - '0'; return f ? (-x) : x; } template<typename T> inline int chkmin(T &a, const T &b){if(b < a) return a = b, 1; return 0;} template<typename T> inline int chkmax(T &a, const T &b){if(b > a) return a = b, 1; return 0;} void renew(int &x, const int &y){ x += y; if(x >= P) x -= P; if(x < 0) x += P; } int Pow(int x, int y, int p){ int a = 1; for (; y; y >>= 1, x = (LL)x * x %p) if(y & 1) a=(LL)a * x%p; return a; } int X[N], Y[N], n; int V[4005][4005], ans, inv[8005], fac[8005]; int C(int x, int y){ return (LL)fac[x + y] * inv[x] % P * inv[y] % P; } int main(){ scanf("%d", &n); REP(i, 0, 8002) inv[i] = Pow(i, P - 2, P); inv[0] = 1; REP(i, 1, 8002) inv[i] = (LL)inv[i - 1] * inv[i] % P; REP(i, 0, 8002) fac[i] = Pow(inv[i], P - 2, P); REP(i, 1, n) scanf("%d%d", X + i, Y + i); REP(i, 1, n) renew(V[2001 - X[i]][2001 - Y[i]], 1); REP(i, 0, 4002) REP(j, 0, 4002){ renew(V[i][j + 1], V[i][j]); renew(V[i + 1][j], V[i][j]); } REP(i, 1, n) renew(ans, V[X[i] + 2001][Y[i] + 2001]); REP(i, 1, n) renew(ans, -C(X[i] + X[i], Y[i] + Y[i])); printf("%d\n", (LL)ans * Pow(2, P - 2, P) % P); return 0; }

codenet

s571382333

p04051

cpp

Accepted

#include<iostream> #include<fstream> #include<sstream> #include<algorithm> #include<cstdio> #include<cctype> #include<cassert> #include<cmath> #include<ctime> #include<cstdlib> #include<cstring> #include<string> #include<queue> #include<vector> #include<map> #include<set> #include<bitset> #include<stack> #include<iomanip> #include<utility> using namespace std; #define mp make_pair #define pb push_back #define X first #define Y second #define rg register #define il inline #define lch(x) ((x)<<1) #define rch(x) ((x)<<1^1) #define eprintf(...) fprintf(stderr,__VA_ARGS__) #define rep0(i,n) for(register int i=0;i<(n);++i) #define per0(i,n) for(register int i=(n)-1;i>=0;--i) #define rep(i,st,ed) for(register int i=(st);i<=(ed);++i) #define per(i,ed,st) for(register int i=(ed);i>=(st);--i) typedef long long ll; typedef unsigned long long ull; typedef unsigned int uint; typedef double dbl; typedef long double ldb; typedef pair<int,int> pii; typedef pair<ll,ll> pll; template<typename T> il T qmin(const T &a,const T &b){return a<b?a:b;} template<typename T> il T qmax(const T &a,const T &b){return a>b?a:b;} template<typename T> il void getmin(T &a,const T &b){if(a>b) a=b;} template<typename T> il void getmax(T &a,const T &b){if(a<b) a=b;} il void fileio(string s){ freopen((s+".in").c_str(),"r",stdin); freopen((s+".out").c_str(),"w",stdout); } const int inf=(int)1e9+7; const ll linf=(ll)1e17+7; const int mod=1e9+7; const int inv2=(mod+1)>>1; const int N=200005; int a[N],b[N],n; int sum[4003][4003]; ll fac[8003],inv[8003]; il int calc(int a,int b){ return fac[a+b]*inv[a]%mod*inv[b]%mod; } il void inc(int &x,const int &y=0){ x+=y; if(x>=mod) x-=mod; } il void dec(int &x,const int &y=0){ x-=y; if(x<0) x+=mod; } int main(){ inv[1]=1; rep(i,2,8000) inv[i]=(mod-mod/i)*inv[mod%i]%mod; fac[0]=inv[0]=1; rep(i,1,8000){ fac[i]=fac[i-1]*i%mod; inv[i]=inv[i-1]*inv[i]%mod; } scanf("%d",&n); rep(i,1,n){ scanf("%d%d",a+i,b+i); ++sum[2000-a[i]][2000-b[i]]; } rep(i,0,4000) rep(j,0,4000){ if(i) inc(sum[i][j],sum[i-1][j]); if(j) inc(sum[i][j],sum[i][j-1]); } int ans=0; rep(i,1,n){ inc(ans,sum[2000+a[i]][2000+b[i]]); dec(ans,calc(a[i]<<1,b[i]<<1)); } ans=(ll)ans*inv[2]%mod; printf("%d\n",ans); return 0; }

codenet

s545230958

p04051

cpp

Accepted

//by yjz #include<bits/stdc++.h> using namespace std; #define FF first #define SS second #define PB push_back #define MP make_pair #define bged(v) (v).begin(),(v).end() #define foreach(it,s) for(__typeof((s).begin()) it=(s).begin();it!=(s).end();it++) typedef long long ll; const int Imx=2147483647; const ll Lbig=2e18; const int mod=1e9+7; //My i/o stream struct fastio { char s[100000]; int it,len; fastio(){it=len=0;} inline char get() { if(it<len)return s[it++];it=0; len=fread(s,1,100000,stdin); if(len==0)return EOF;else return s[it++]; } bool notend() { char c=get(); while(c==' '||c=='\n')c=get(); if(it>0)it--; return c!=EOF; } }_buff; #define geti(x) x=getnum() #define getii(x,y) geti(x),geti(y) #define getiii(x,y,z) getii(x,y),geti(z) #define puti(x) putnum(x),putchar(' ') #define putii(x,y) puti(x),puti(y) #define putiii(x,y,z) putii(x,y),puti(z) #define putsi(x) putnum(x),putchar('\n') #define putsii(x,y) puti(x),putsi(y) #define putsiii(x,y,z) putii(x,y),putsi(z) inline ll getnum() { ll r=0;bool ng=0;char c;c=_buff.get(); while(c!='-'&&(c<'0'||c>'9'))c=_buff.get(); if(c=='-')ng=1,c=_buff.get(); while(c>='0'&&c<='9')r=r*10+c-'0',c=_buff.get(); return ng?-r:r; } template<class T> inline void putnum(T x) { if(x<0)putchar('-'),x=-x; register short a[20]={},sz=0; while(x)a[sz++]=x%10,x/=10; if(sz==0)putchar('0'); for(int i=sz-1;i>=0;i--)putchar('0'+a[i]); } inline char getreal(){char c=_buff.get();while(c==' '||c=='\n')c=_buff.get();return c;} int n,a[200111],b[200111]; ll C[4011][4011],dp[4011][4011]; ll qpow(ll x,ll k){return k==0?1:qpow(x*x%mod,k>>1)*(k&1?x:1)%mod;} int main() { for(int i=0;i<=4004;i++)C[i][0]=C[0][i]=1; for(int i=1;i<=4004;i++) { for(int j=1;j<=4004;j++) { C[i][j]=(C[i-1][j]+C[i][j-1])%mod; } } geti(n); for(int i=1;i<=n;i++) { getii(a[i],b[i]); dp[2002-a[i]][2002-b[i]]++; // cerr<<a[i]<<" "<<b[i]<<" "<<C[a[i]][b[i]]<<endl; } for(int i=1;i<=4010;i++) { for(int j=1;j<=4010;j++) { dp[i][j]=(dp[i][j]+dp[i-1][j]+dp[i][j-1])%mod; } } ll ans=0; for(int i=1;i<=n;i++) { // cerr<<dp[2002+a[i]][2002+b[i]]<<endl; ans=(ans+dp[2002+a[i]][2002+b[i]])%mod; ans=(ans-C[2*a[i]][2*b[i]]+mod)%mod; } cout<<ans*qpow(2,mod-2)%mod<<endl; return 0; }

codenet

s743564554

p04051

cpp

Accepted

#include <iostream> #include <vector> #include <string> #include <algorithm> #include <cstdio> #include <numeric> #include <cstring> #include <ctime> #include <cstdlib> #include <set> #include <map> #include <unordered_map> #include <unordered_set> #include <list> #include <cmath> #include <bitset> #include <cassert> #include <queue> #include <deque> #include <cassert> #define pb push_back #define x first #define y second #define files(FileName) read(FileName); write(FileName) #define read(FileName) freopen((FileName + ".in").c_str(), "r", stdin) #define write(FileName) freopen((FileName + ".out").c_str(), "w", stdout) using namespace std; template<typename T1, typename T2>inline void chkmin(T1 &x, T2 y) { if (x > y) x = y; } template<typename T1, typename T2>inline void chkmax(T1 &x, T2 y) { if (x < y) x = y; } const string FILENAME = "input"; const int MAXN = 4e3 + 5, H = 2e3 + 1, p = 1e9 + 7; typedef pair <int, int> point; int sum(int a, int b) { a += b; if (a >= p) return a - p; return a; } int mul(long long a, int b) { return a * b % p; } int powx(int a, int b) { int ans = 1; while (b) { if (b & 1) ans = mul(ans, a); a = mul(a, a); b >>= 1; } return ans; } const int p2 = powx(2, p - 2); int n; int f[2][MAXN * 2]; vector <point> arr; int dp[MAXN][MAXN]; int ans = 0; int cnk(int n, int k) { return mul(f[0][n], mul(f[1][n - k], f[1][k])); } int main() { ios::sync_with_stdio(false); srand(time(0)); //read(FILENAME); f[0][0] = 1; f[1][0] = 1; for (int i = 1; i < MAXN * 2; ++i) { f[0][i] = mul(f[0][i - 1], i); f[1][i] = powx(f[0][i], p - 2); } cin >> n; arr.resize(n); for (int i = 0; i < n; ++i) { cin >> arr[i].x >> arr[i].y; ++dp[H - arr[i].x][H - arr[i].y]; } for (int i = 0; i + 1 < MAXN; ++i) { for (int j = 0; j + 1 < MAXN; ++j) { dp[i][j + 1] = sum(dp[i][j], dp[i][j + 1]); dp[i + 1][j] = sum(dp[i][j], dp[i + 1][j]); } } for (auto i : arr) { ans = sum(ans, dp[H + i.x][H + i.y]); ans = sum(ans, p - cnk((i.x + i.y) * 2, i.x * 2)); } // for (int i = 0; i < n; ++i) { // for (int j = 0; j < n; ++j) { // if (i == j) continue; // ans = sum(ans, cnk(arr[i].x + arr[i].y + arr[j].x + arr[j].y, arr[i].x + arr[j].x)); // } // } cout << mul(ans, p2) << endl; }

codenet

s760332228

p04051

cpp

Accepted

//84104971101048411497 - Can you guess what does this mean? #include <bits/stdc++.h> using namespace std; typedef long long ll; typedef complex<double> point; #define mapii map<int, int> #define debug(a) cout << #a << ": " << a << endl #define debuga1(a, l, r) fto(i, l, r) cout << a[i] << " "; cout << endl #define fdto(i, r, l) for(int i = (r); i >= (l); --i) #define fto(i, l, r) for(int i = (l); i <= (r); ++i) #define forit(it, var) for(__typeof(var.begin()) it = var.begin(); it != var.end(); it++) #define forrit(rit, var) for(__typeof(var.rbegin()) rit = var.rbegin(); rit != var.rend(); rit++) #define ii pair<int, int> #define iii pair<int, ii> #define ff first #define ss second #define mp make_pair #define pb push_back #define X real() #define Y imag() #define maxN 200005 #define maxX 2000 #define oo 2000000007 #define EPS 1e-9 #define MOD 1000000007 const double PI = acos(-1.0); double fRand(double fMin, double fMax) { double f = (double)rand() / RAND_MAX; return fMin + f * (fMax - fMin); } template <class T> T min(T a, T b, T c) { return min(a, min(b, c)); } template <class T> T max(T a, T b, T c) { return max(a, max(b, c)); } int power(int x, int n) { if (n == 0) return 1; if (n&1) return ((ll)x*power(x, n-1))%MOD; int p = power(x, n/2); return ((ll)p*p)%MOD; } void add(int &a, int b) {a = (a+b)%MOD;} int n, a[maxN], b[maxN], cnt[2*maxX+1][2*maxX+1], dp[2*maxX+1][2*maxX+1], fact[4*maxX+1], invFact[4*maxX+1]; int C(int n, int k) { ll t = ((ll)fact[n]*invFact[k])%MOD; return (t*invFact[n-k])%MOD; } int main () { scanf("%d", &n); fto(i, 1, n) { scanf("%d%d", &a[i], &b[i]); ++cnt[maxX-a[i]][maxX-b[i]]; } fact[0] = invFact[0] = 1; fto(i, 1, 4*maxX) { fact[i] = ((ll)fact[i-1]*i)%MOD; invFact[i] = power(fact[i], MOD-2); } fto(x, 0, 2*maxX) { fto(y, 0, 2*maxX) { dp[x][y] = cnt[x][y]; if (x > 0) add(dp[x][y], dp[x-1][y]); if (y > 0) add(dp[x][y], dp[x][y-1]); } } int ans = 0; fto(i, 1, n) { add(ans, dp[maxX+a[i]][maxX+b[i]]); add(ans, MOD-C(2*(a[i]+b[i]), 2*a[i])); } ans = ((ll)ans*power(2, MOD-2))%MOD; printf("%d", ans); return 0; }

codenet

s409506315

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; using ll = long long; using ld = long double; using vl = vector<ll>; template<class T> using vc = vector<T>; template<class T> using vvc = vector<vector<T>>; const ll MOD = 1e9 + 7; // const ll MOD = 998244353; const ll INF = 1e16; const ld EPS = 1e-11; const ld PI = acos(-1.0L); #define eb emplace_back #define all(x) (x).begin(), (x).end() #define rep(i, n) for (ll i = 0; i < (n); i++) #define repr(i, n) for (ll i = (n)-1; i >= 0; i--) #define repe(i, l, r) for (ll i = (l); i < (r); i++) #define reper(i, l, r) for (ll i = (r)-1; i >= (l); i--) template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; } template<class T> bool chmin(T &a, const T &b) { if (b<a) { a=b; return 1; } return 0; } void init() {cin.tie(0);ios::sync_with_stdio(false);cout << fixed << setprecision(15);} //--------------------------------------------------------------------------------// ll modpow(ll a, ll n, ll mod_) { ll res = 1; while (n > 0) { if (n & 1) res = res * a % mod_; a = a * a % mod_; n >>= 1; } return res; } const ll MAX_SIZE = 10005; array<ll, MAX_SIZE> fac, inv, finv; void fac_init() { // combination init fac[0] = 1; for (ll i = 1; i < MAX_SIZE; i++) fac[i] = fac[i - 1] * i % MOD; finv[0] = modpow(fac[MAX_SIZE - 1], MOD - 2, MOD); repe(i, 1, MAX_SIZE) finv[i] = finv[i - 1] * (MAX_SIZE - i) % MOD; reverse(all(finv)); //inv init repe(i, 1, MAX_SIZE) inv[i] = modpow(i, MOD - 2, MOD); } ll perm(ll a, ll b) { return fac[a] * finv[a - b] % MOD; } ll comb(ll a, ll b) { return fac[a] * finv[b] % MOD * finv[a - b] % MOD; } const ll AB = 2000; ll dp[AB*2 + 5][AB*2 + 5]; int main() { init(); fac_init(); ll N; cin >> N; vl A(N), B(N); rep(i, N) cin >> A[i] >> B[i]; rep(i, N) dp[AB - A[i]][AB - B[i]] += 1; rep(a,AB*2+1)rep(b,AB*2+1){ dp[a][b] %= MOD; ll v = dp[a][b]; dp[a + 1][b] += v; dp[a][b + 1] += v; } ll ans = 0; rep(i,N){ ll a = A[i], b = B[i]; ans += dp[AB + a][AB + b]; ans -= comb(2 * (a + b), 2 * a); ans = (ans % MOD + MOD) % MOD; } ans *= inv[2]; ans %= MOD; cout << ans << endl; }

codenet

s147592103

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; typedef long long ll; typedef pair<ll, ll> l_l; typedef pair<int, int> i_i; template<class T> inline bool chmax(T &a, T b) { if(a < b) { a = b; return true; } return false; } template<class T> inline bool chmin(T &a, T b) { if(a > b) { a = b; return true; } return false; } #define EPS (1e-7) #define INF (1e9) #define PI (acos(-1)) const ll mod = 1000000007; ll inv[100100]; ll FactorialInv[100100]; ll Factorial[100100]; ll beki(ll a, ll b){ if(b == 0){ return 1; } ll ans = beki(a, b / 2); ans = ans * ans % mod; if(b % 2 == 1){ ans = ans * a % mod; } return ans; } void init_combination(){ const int MAX = 10002; Factorial[0] = 1; inv[0] = 1; for(int i = 1; i <= MAX; i++){ Factorial[i] = Factorial[i - 1] * i % mod; } FactorialInv[MAX] = beki(Factorial[MAX], mod - 2); for(ll i = MAX - 1; i >= 0; i--) { FactorialInv[i] = FactorialInv[i+1] * (i+1) % mod; } for(int i = 1; i <= MAX; i++) { inv[i] = FactorialInv[i] * Factorial[i-1] % mod; } } ll combination(ll a, ll b){ if((a == b) || (b == 0)){ return 1; } if(a < b) return 0; ll ans = Factorial[a] * FactorialInv[b] % mod; ans = ans * FactorialInv[a - b] % mod; return ans; } int N; int dp[4005][4005]; int A[200050], B[200050]; int main() { //cout.precision(10); cin.tie(0); ios::sync_with_stdio(false); cin >> N; init_combination(); for(int i = 1; i <= N; i++) { cin >> A[i] >> B[i]; dp[2000-A[i]][2000-B[i]]++; } for(int i = 0; i <= 4000; i++) { for(int j = 0; j <= 4000; j++) { if(i > 0) dp[i][j] += dp[i-1][j]; dp[i][j] %= mod; if(j > 0) dp[i][j] += dp[i][j-1]; dp[i][j] %= mod; } } ll ans = 0; for(int i = 1; i <= N; i++) { ans += dp[2000+A[i]][2000+B[i]]; ans %= mod; ans -= combination(2*A[i]+2*B[i], 2*A[i]); ans %= mod; ans += mod; ans %= mod; } //ans *= beki(2, mod - 2); //ans %= mod; ll answer = (ll)ans * beki(2, mod - 2); answer %= mod; cout << answer << endl; return 0; }

codenet

s181478958

p04051

cpp

Accepted

# include <bits/stdc++.h> using namespace std; # define fi cin # define fo cout # define x first # define y second # define ll long long # define db long double # define scn(x) scanf("%I64d",&x) # define scan(x) scanf("%d",&x) # define print(x) printf("%d ",x) # define prnt(x) printf("%I64d ",x); # define eol printf("\n") # define IOS ios_base :: sync_with_stdio(0) # define pe "Possible" # define ie "Impossible" # define halt(...) {fo << (__VA_ARGS__) << '\n';exit(0);} # define rep1(n) for (int qwerty = 1;qwerty <= n;++qwerty) # define CF # ifdef CF # define DEBUG # endif // CF # ifdef DEBUG # define pp(n) cerr << #n << " = " << n << '\n' # define ppp(v) for (auto it : v) cerr << it << ' ';cerr << '\n' # define aprint(x,y,z) for (int i = x;i <= y;++i) cerr << z[i] << ' ';cerr << '\n' # else # define pp(n) ; # define ppp(v) ; # define aprint(x,y,z); # endif // DEBUG # define rep(n) for (int i = 1;i <= n;++i) const int mod = 1e9 + 7; int dp[4015][4015]; int f[1 << 20]; int c[1 << 20]; int pow(int a,int b,int mod) { int ans = 1; while (b) { if (b&1) ans = (1ll * ans * a) % mod; a = (1ll * a * a) % mod; b /= 2; } return ans; } int main(void) { # ifdef CF # endif // CF srand(time(0)); fo << fixed << setprecision(7); cerr << fixed << setprecision(7); int n; IOS; fi>>n; vector < pair < int , int > > want; for (int i = 1;i <= n;++i) { int a,b; fi>>a>>b; dp[2000 - a][2000 - b] += 1; want.push_back({a,b}); } for (int i = 0;i < 4003;++i) for (int j = 0;j < 4003;++j) dp[i+1][j] = (dp[i+1][j] + dp[i][j]) % mod, dp[i][j+1] = (dp[i][j] + dp[i][j+1]) % mod; f[0] = c[0] = 1; for (int i = 1;i <= 1e5;++i) { f[i] = (1ll * f[i-1] * i) % mod; c[i] = pow(f[i],mod - 2,mod); } auto C = [&](int n,int k) { int ans = (1ll * f[n] * c[k]) % mod; ans = (1ll * ans * c[n - k]) % mod; return ans; }; int ans = 0; for (auto it : want) ans = (ans + dp[it.x + 2000][it.y + 2000]) % mod; for (auto it : want) ans = (ans + mod - 1ll * C((it.x+it.y) << 1,it.x << 1)) % mod; ans = (ans * 1ll * pow(2,mod - 2,mod)) % mod; fo << ans << '\n'; return 0; }

codenet

s345577625

p04051

cpp

Accepted

#ifdef DEBUG #define _GLIBCXX_DEBUG #endif #include <bits/stdc++.h> using namespace std; typedef long double ld; #ifdef DEBUG #define eprintf(...) fprintf(stderr, __VA_ARGS__), fflush(stderr) #else #define eprintf(...) ; #endif #define sz(x) ((int) (x).size()) #define TASK "text" const int inf = (int) 1.01e9; const long long infll = (long long) 1.01e18; const ld eps = 1e-9; const ld pi = acos((ld) -1); #ifdef DEBUG mt19937 mrand(300); #else mt19937 mrand(chrono::steady_clock::now().time_since_epoch().count()); #endif int rnd(int x) { return mrand() % x; } const int mod = (int) 1e9 + 7; int mul(int a, int b) { return (long long) a * b % mod; } void add(int &a, int b) { a += b; if (a >= mod) { a -= mod; } } const int maxm = (int) 1e4 + 5; int f[maxm], inv[maxm], finv[maxm]; void precalc() { f[0] = 1; for (int i = 1; i < maxm; i++) { f[i] = mul(f[i - 1], i); } inv[1] = 1; for (int i = 2; i < maxm; i++) { inv[i] = (mod - (long long) (mod / i) * inv[mod % i] % mod) % mod; } finv[0] = 1; for (int i = 1; i < maxm; i++) { finv[i] = mul(finv[i - 1], inv[i]); } } int c(int n, int k) { return mul(f[n], mul(finv[n - k], finv[k])); } const int maxn = (int) 2e5 + 5; int n; int a[maxn], b[maxn]; bool read() { if (scanf("%d", &n) < 1) { return false; } for (int i = 0; i < n; i++) { scanf("%d%d", &a[i], &b[i]); b[i] += a[i]; } return true; } const int X = 2005, maxx = 2 * X + 1; int s[maxx][maxx]; void solve() { memset(s, 0, sizeof(s)); for (int i = 0; i < n; i++) { int l = X + a[i] - b[i], r = X + a[i]; add(s[r - l][l], 1); } for (int i = maxx - 2; i >= 0; i--) { for (int j = 0; j < maxx; j++) { add(s[i][j], s[i + 1][j]); if (j) { add(s[i][j], s[i + 1][j - 1]); } } } int res = 0; for (int i = -X; i < X; i++) { add(res, mul(s[0][X + i], s[0][X - i])); } for (int i = 0; i < n; i++) { add(res, mod - c(2 * b[i], 2 * a[i])); } res = mul(res, (mod + 1) / 2); printf("%d\n", res); } int main() { precalc(); #ifdef DEBUG assert(freopen(TASK ".in", "r", stdin)); assert(freopen(TASK ".out", "w", stdout)); #endif while (read()) { solve(); #ifdef DEBUG eprintf("Time %.2f\n", (double) clock() / CLOCKS_PER_SEC); #endif } return 0; }

codenet

s969908136

p04051

cpp

Accepted

#include <vector> #include <iostream> #include <algorithm> #include <string> using namespace std; const int MOD = 1e9 + 7; inline void ModSum(int& x, int y) { x += y; if (x >= MOD) { x -= MOD; } if (x < 0) { x += MOD; } } inline int GetModSum(int x, int y) { ModSum(x, y); return x; } inline void ModMul(int& x, int y) { x = (1LL * x * y) % MOD; } inline int GetModMul(int x, int y) { ModMul(x, y); return x; } int GetBinaryPow(int x, int pw) { int result = 1; while (pw > 0) { if (pw & 1) { ModMul(result, x); } ModMul(x, x); pw >>= 1; } return result; } int GetInv(int x) { return GetBinaryPow(x, MOD - 2); } #define LLD_SPEC "%lld" const int BASE = 2e3; const int COORD_COUNT = 2 * BASE + 1; const int MAX_FACT = 4 * BASE + 1; int fact[MAX_FACT]; int invFact[MAX_FACT]; void BuildFact() { fact[0] = 1; for (int i = 1; i < MAX_FACT; ++i) { fact[i] = fact[i - 1]; ModMul(fact[i], i); } for (int i = 0; i < MAX_FACT; ++i) { invFact[i] = GetInv(fact[i]); } } int GetC(int n, int k) { if (k > n) { return 0; } int result = fact[n]; ModMul(result, invFact[k]); ModMul(result, invFact[n - k]); return result; } int main() { BuildFact(); int n; scanf("%d", &n); vector<pair<int, int>> a(n); for (int i = 0; i < n; ++i) { scanf("%d%d", &a[i].first, &a[i].second); } vector<vector<int>> sum(COORD_COUNT, vector<int>(COORD_COUNT, 0)); for (int i = 0; i < n; ++i) { ++sum[BASE - a[i].first][BASE - a[i].second]; } for (int j = 1; j < COORD_COUNT; ++j) { ModSum(sum[0][j], sum[0][j - 1]); } for (int i = 1; i < COORD_COUNT; ++i) { ModSum(sum[i][0], sum[i - 1][0]); } for (int i = 1; i < COORD_COUNT; ++i) { for (int j = 1; j < COORD_COUNT; ++j) { ModSum(sum[i][j], sum[i - 1][j]); ModSum(sum[i][j], sum[i][j - 1]); } } int result = 0; for (int i = 0; i < n; ++i) { ModSum(result, sum[a[i].first + BASE][a[i].second + BASE]); ModSum(result, -GetC(2 * (a[i].first + a[i].second), 2 * a[i].first)); } ModMul(result, GetInv(2)); printf("%d\n", result); return 0; }

codenet

s100619186

p04051

cpp

Accepted

#include <bits/stdc++.h> #define be(v) (v).begin(),(v).end() #define pb(q) push_back(q) typedef long long ll; using namespace std; const ll mod=1000000007, INF=mod*mod*3LL; #define doublecout(a) cout<<fixed<<setprecision(10)<<a<<endl; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} ll fac[10000],finv[10000],inv[10000]; void cominit(){ fac[0]=fac[1]=1; finv[0]=finv[1]=1; inv[1]=1; for(int i=2;i<10000;i++){ fac[i]=fac[i-1]*i%mod; inv[i]=mod-inv[mod%i]*(mod/i)%mod; finv[i]=finv[i-1]*inv[i]%mod; } } ll com(ll n,ll k){ if(n<k)return 0; if(n<0 || k<0)return 0; return fac[n]*(finv[k]*finv[n-k]%mod)%mod; } mint dp[4005][4005]; int main() { cin.tie(0); cout.tie(0); ios::sync_with_stdio(false); cominit(); ll n, a, b, N = 2001; cin >> n; vector<pair<ll,ll> > v; for(int i=0;i<n;i++) { cin >> a >> b; dp[N - a][N - b] += 1; v.push_back({a,b}); } mint ans = 0; ll M = N * 2; for(int i=1;i<=M;i++){ for(int j=1;j<=M;j++){ dp[i][j] += dp[i-1][j] + dp[i][j-1]; } } for(auto& i:v){ ans += dp[i.first + N][i.second + N]; ans -= com( i.first * 2 + i.second * 2, i.first * 2); } ans /= 2; cout << ans << endl; return 0; }

codenet

s009828317

p04051

cpp

Accepted

#include <bits/stdc++.h> #define long long long #define ull unsigned long long #define up(i,a,b) for (int i=a; i<=b; i++) #define upadj(i,adj) if (adj.size()>0) up(i,0,adj.size()-1) #define down(i,a,b) for (int i=a; i>=b; i--) #define endl '\n' #define pb push_back #define X first #define Y second #define II pair<int, int> #define III pair<int, pair<int, int> > #define V vector #define debug(X) cerr<< #X << "=" <<X << endl #define debug2(X,Y) cerr<< #X << "=" <<X << ", " << #Y << "=" <<Y << endl #define show(X,a,b) {cerr << #X << " = "; up(__,a,b) cerr << X[__] << ' '; cerr << endl;} #define gc getchar #define pc putchar using namespace std; inline void read(int &x) { register int c = gc(); x = 0; int neg = 0; for (;((c<48 || c>57) && c != '-') ;c = gc()); if(c=='-') {neg=1;c=gc();} for(;c>47 && c<58;c = gc()) {x = (x<<1) + (x<<3) + c - 48;} if(neg) x=-x; } inline void writeln(int x){ char buffor[21]; register int i=0; int neg=0; if (x<0) {neg=1; x= -x;} do{ buffor[i++]=(x%10)+'0'; x/=10; } while(x); i--; if (neg) pc('-'); while(i>=0) pc(buffor[i--]); pc('\n'); } const int base= 1e9+ 7; const int M= 2001; int n,a[200010],b[200010],f[4003][4003]; int res; int Add(int a,int b) { return (a+b>= base)?a+b-base: a+b; } int Sub(int a,int b) { return (a-b<0)?a-b+base: a-b; } void input() { cin>>n; up(i,1,n) cin>>a[i]>> b[i]; } long power(int x,int k) { if (k==1) return x; long t= power(x,k/2); t= t*t% base; if (k%2==1) t= t*x%base; return t; } void solve() { up(i,1,n) f[-a[i]+M][-b[i]+M]++;// ( -a,-b) up(x,-2000,2000) up(y,-2000,2000) f[x+M][y+M]= Add(f[x+M][y+M], Add(f[x-1+M][y+M],f[x+M][y-1+M]) ); res= 0; up(i,1,n) res= Add(res, f[a[i]+M][b[i]+M]); up(x,0,4000) f[x][0]= 1; up(y,0,4000) f[0][y]= 1; up(x,1,4000) up(y,1,4000) f[x][y]= Add(f[x-1][y],f[x][y-1]); up(i,1,n) res= Sub(res, f[a[i]+a[i]][b[i]+b[i]]); cout<<res* power(2,base-2)% base; } int main() { ios_base::sync_with_stdio(false); cin.tie(NULL); #ifdef I_Love_Pork #define TASK "tmp" freopen(TASK".inp","r",stdin); freopen(TASK".out","w",stdout); #endif input(); solve(); return 0; }

codenet

s084803709

p04051

cpp

Accepted

#ifndef ___CLASS_MODINT #define ___CLASS_MODINT #include <cstdint> template<std::uint32_t mod> class modint { private: std::uint32_t n; public: modint() : n(0) {}; modint(std::uint64_t n_) : n(n_ % mod) {}; bool operator==(const modint& m) const { return n == m.n; } bool operator!=(const modint& m) const { return n != m.n; } std::uint32_t get() const { return n; } modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; } modint operator+(const modint& m) const { return modint(*this) += m; } modint operator-(const modint& m) const { return modint(*this) -= m; } modint operator*(const modint& m) const { return modint(*this) *= m; } modint binpow(std::uint64_t b) const { modint ans = 1, m = modint(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } modint inv() { return (*this).binpow(mod - 2); } }; #endif // ___CLASS_MODINT #include <vector> #include <iostream> #include <algorithm> using namespace std; using modulo = modint<1000000007>; int main() { int N; cin >> N; vector<int> A(N), B(N); int la = 0, lb = 0; for (int i = 0; i < N; ++i) { cin >> A[i] >> B[i]; la = max(la, A[i]); lb = max(lb, B[i]); } vector<vector<modulo> > dp(la + 1, vector<modulo>(lb + 1)), comb(la * 2 + 1, vector<modulo>(lb * 2 + 1)); comb[0][0] = 1; for (int i = 0; i <= la * 2; ++i) { for (int j = 0; j <= lb * 2; ++j) { if (i >= 1) comb[i][j] += comb[i - 1][j]; if (j >= 1) comb[i][j] += comb[i][j - 1]; } } for (int i = 0; i < N; ++i) { dp[A[i]][B[i]] += 1; } for (int i = la; i >= 1; --i) { for (int j = lb; j >= 1; --j) { dp[i - 1][j] += dp[i][j]; dp[i][j - 1] += dp[i][j]; } } modulo ans = 0; for (int i = 1; i <= la; ++i) { for (int j = 1; j <= la; ++j) { ans += dp[i][0] * dp[j][0]; } } for (int i = 1; i <= lb; ++i) { for (int j = 1; j <= lb; ++j) { ans += dp[0][i] * dp[0][j]; } } for (int i = 1; i <= la; ++i) { for (int j = 1; j <= lb; ++j) { ans += dp[i][0] * dp[0][j] * comb[i][j] * 2; } } for (int i = 0; i < N; ++i) { ans -= comb[A[i] * 2][B[i] * 2]; } ans *= modulo(2).inv(); cout << ans.get() << endl; return 0; }

codenet

s084803709

p04051

cpp

Accepted

#ifndef ___CLASS_MODINT #define ___CLASS_MODINT #include <cstdint> template<std::uint32_t mod> class modint { private: std::uint32_t n; public: modint() : n(0) {}; modint(std::uint64_t n_) : n(n_ % mod) {}; bool operator==(const modint& m) const { return n == m.n; } bool operator!=(const modint& m) const { return n != m.n; } std::uint32_t get() const { return n; } modint& operator+=(const modint& m) { n += m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator-=(const modint& m) { n += mod - m.n; n = (n < mod ? n : n - mod); return *this; } modint& operator*=(const modint& m) { n = std::uint64_t(n) * m.n % mod; return *this; } modint operator+(const modint& m) const { return modint(*this) += m; } modint operator-(const modint& m) const { return modint(*this) -= m; } modint operator*(const modint& m) const { return modint(*this) *= m; } modint binpow(std::uint64_t b) const { modint ans = 1, m = modint(*this); while (b) { if (b & 1) ans *= m; m *= m; b >>= 1; } return ans; } modint inv() { return (*this).binpow(mod - 2); } }; #endif // ___CLASS_MODINT #include <vector> #include <iostream> #include <algorithm> using namespace std; using modulo = modint<1000000007>; int main() { int N; cin >> N; vector<int> A(N), B(N); int la = 0, lb = 0; for (int i = 0; i < N; ++i) { cin >> A[i] >> B[i]; la = max(la, A[i]); lb = max(lb, B[i]); } vector<vector<modulo> > dp(la + 1, vector<modulo>(lb + 1)), comb(la * 2 + 1, vector<modulo>(lb * 2 + 1)); comb[0][0] = 1; for (int i = 0; i <= la * 2; ++i) { for (int j = 0; j <= lb * 2; ++j) { if (i >= 1) comb[i][j] += comb[i - 1][j]; if (j >= 1) comb[i][j] += comb[i][j - 1]; } } for (int i = 0; i < N; ++i) { dp[A[i]][B[i]] += 1; } for (int i = la; i >= 1; --i) { for (int j = lb; j >= 1; --j) { dp[i - 1][j] += dp[i][j]; dp[i][j - 1] += dp[i][j]; } } modulo ans = 0; for (int i = 1; i <= la; ++i) { for (int j = 1; j <= la; ++j) { ans += dp[i][0] * dp[j][0]; } } for (int i = 1; i <= lb; ++i) { for (int j = 1; j <= lb; ++j) { ans += dp[0][i] * dp[0][j]; } } for (int i = 1; i <= la; ++i) { for (int j = 1; j <= lb; ++j) { ans += dp[i][0] * dp[0][j] * comb[i][j] * 2; } } for (int i = 0; i < N; ++i) { ans -= comb[A[i] * 2][B[i] * 2]; } ans *= modulo(2).inv(); cout << ans.get() << endl; return 0; }

codenet

s329474692

p04051

cpp

Accepted

#include "bits/stdc++.h" #define MOD 1000000007 #define inf 0x3f3f3f3f3f3f3f3f #define pi acos(-1.0) #define ri register int #define Abs(x) ((x) < 0 ? (-(x)) : (x)) #define int long long const int maxn = 4e3 + 20, delta = 2005; inline int Max(int a, int b) { return a > b ? a : b; } inline int Min(int a, int b) { return a > b ? b : a; } namespace FastIO { inline int read() { int f = 1, r = 0; char c = getchar(); while (!isdigit(c)) { if (c == '-') { f = -1; } c = getchar(); } while (isdigit(c)) { r = 10 * r + c - '0'; c = getchar(); } return f * r; } inline void write(int x) { if (x < 0) putchar('-'), x = -x; if (x > 9) write(x / 10); putchar(x % 10 + '0'); } inline void writesp(int x) { write(x), putchar(' '); } inline void writeln(int x) { write(x), puts(""); } }; using namespace FastIO; int fac[maxn * 2], N, arr[200000 + 10][2], dp[maxn][maxn], invv[maxn * 2]; inline int exgcd(int a, int b, int& x, int& y) { if (b == 0) { x = 1, y = 0; return a; } int d = exgcd(b, a % b, x, y); int tmp = y; y = x - a / b * y; x = tmp; return d; } inline int inv(int a, int b) { int x, y; exgcd(a, b, x, y); return (x + MOD) % MOD; } signed main() { //freopen("C:\Users\hjw\Downloads\testdata (4).in", "r", stdin); N = read(); for (ri i = 1; i <= N; ++i) { arr[i][0] = read(), arr[i][1] = read(), dp[-arr[i][0] + delta][-arr[i][1] + delta]++; } for (ri i = -2000 + delta; i <= 2000 + delta; ++i) { for (ri j = -2000 + delta; j <= 2000 + delta; ++j) { dp[i][j] = (dp[i - 1][j] + dp[i][j] + dp[i][j - 1]) % MOD; } } fac[0] = 1; for (ri i = 1; i < maxn * 2; ++i) { fac[i] = fac[i - 1] * i % MOD; } for (ri i = 0; i < maxn * 2; ++i) { invv[i] = inv(fac[i], MOD); } int ans = 0; for (ri i = 1; i <= N; ++i) { int down = 2 * (arr[i][0] + arr[i][1]), up = 2 * arr[i][0]; int tmp = fac[down] * invv[down - up] % MOD * invv[up] % MOD; ans = (ans + tmp) % MOD; } int sum = 0; for (ri i = 1; i <= N; ++i) { sum = (sum + dp[arr[i][0] + delta][arr[i][1] + delta]) % MOD; } sum = (sum - ans + MOD) % MOD; sum = (sum * inv(2, MOD)) % MOD; writeln(sum); return 0; }

codenet

s851669643

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define pb push_back #define mp make_pair typedef long long ll; typedef pair<int, int> pii; typedef vector<int> vi; typedef complex<double> point; #define xx real() #define yy imag() #define REP(i, a, b) for(int i = (a); i < (int)(b); i++) #define REPN(i, a, b) for(int i = (a); i <= (int)(b); i++) #define FA(it, x) for(__typeof((x).begin()) it = (x).begin(); it != (x).end(); it++) #define SZ(x) (int)(x).size() #define BE(x) (x).begin(), (x).end() #define SORT(x) sort(BE(x)) #define _1 first #define _2 second #define x1 gray_cat_x1 #define y1 gray_cat_y1 template<class T> T gcd(T a, T b) { return b ? gcd(b, a % b) : a; } #define file "cycle" const double EPS = 1e-9; const double PI = acos(-1.); const int INF = 1e9; const ll MOD = 1e9 + 7; const int MAXN = 2e5 + 5, MAXV = 2003; int dp[2 * MAXV][2 * MAXV]; int a[MAXN], b[MAXN]; ll f[4 * MAXV], _f[4 * MAXV]; int cnt[2 * MAXV][2 * MAXV]; ll pow_mod(ll a, ll st){ ll ans = 1ll; for(; st; st >>= 1){ if (st & 1){ ans = (ans * a) % MOD; } a = (a * a) % MOD; } return ans; } void solve(){ int n; scanf("%d", &n); REP(i, 0, n){ scanf("%d%d", &a[i], &b[i]); } f[0] = 1; REP(i, 1, 4 * MAXV){ f[i] = (f[i - 1] * i) % MOD; } _f[4 * MAXV - 1] = pow_mod(f[4 * MAXV - 1], MOD - 2); for(int i = 4 * MAXV - 2; i >= 0; i--){ _f[i] = (_f[i + 1] * (i + 1)) % MOD; } int offset = 2000; REP(i, 0, n){ cnt[offset - a[i]][offset - b[i]]++; } ll ans = 0ll; REP(i, 0, 2 * MAXV){ REP(j, 0, 2 * MAXV){ if (i){ dp[i][j] = dp[i - 1][j]; } if (j){ dp[i][j] += dp[i][j - 1]; } dp[i][j] += cnt[i][j]; if (dp[i][j] >= MOD){ dp[i][j] -= MOD; if (dp[i][j] >= MOD){ dp[i][j] -= MOD; } } if (i >= offset && j >= offset){ if (2 * offset - i >= 0 && 2 * offset - j >= 0){ ans = (ans + (ll)cnt[2 * offset - i][2 * offset - j] * (ll)dp[i][j]) % MOD; } } } } REP(i, 0, n){ ll c = (f[a[i] + a[i] + b[i] + b[i]] * _f[a[i] + a[i]]) % MOD; c = (c * _f[b[i] + b[i]]) % MOD; //cout << a[i] + a[i] + b[i] + b[i] << " " << a[i] + a[i] << " " << c << endl; ans = (ans + MOD - c) % MOD; } ll tmp = (MOD + 1) / 2; ans = (ans * tmp) % MOD; cout << ans << endl; } int main(){ //freopen(file".in", "r", stdin); freopen(file".out", "w", stdout); int t = 1; //cin >> t; while(t--){ solve(); } }

codenet

s712074402

p04051

cpp

Accepted

/************************************************ * Au: Hany01 * Prob: agc001e * Email: hany01dxx@gmail.com & hany01@foxmail.com * Inst: Yali High School ************************************************/ #include<bits/stdc++.h> using namespace std; typedef long long LL; typedef long double LD; typedef pair<int, int> PII; #define Rep(i, j) for (register int i = 0, i##_end_ = (j); i < i##_end_; ++ i) #define For(i, j, k) for (register int i = (j), i##_end_ = (k); i <= i##_end_; ++ i) #define Fordown(i, j, k) for (register int i = (j), i##_end_ = (k); i >= i##_end_; -- i) #define Set(a, b) memset(a, b, sizeof(a)) #define Cpy(a, b) memcpy(a, b, sizeof(a)) #define X first #define Y second #define PB(a) push_back(a) #define MP(a, b) make_pair(a, b) #define SZ(a) ((int)(a).size()) #define ALL(a) a.begin(), a.end() #define INF (0x3f3f3f3f) #define INF1 (2139062143) #define debug(...) fprintf(stderr, __VA_ARGS__) #define y1 wozenmezhemecaia template <typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, 1 : 0; } template <typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, 1 : 0; } template <typename T> inline T read() { static T _, __; static char c_; for (_ = 0, __ = 1, c_ = getchar(); c_ < '0' || c_ > '9'; c_ = getchar()) if (c_ == '-') __ = -1; for ( ; c_ >= '0' && c_ <= '9'; c_ = getchar()) _ = (_ << 1) + (_ << 3) + (c_ ^ 48); return _ * __; } //EOT const int maxn = 2e5 + 5, maxm = 4007, MOD = 1e9 + 7, M = 4005, N = 2002; int n, A[maxn], B[maxn], dp[maxm][maxm], fac[maxm << 1], ifac[maxm << 1], ans; inline int Pow(int a, LL b) { register int ans = 1; for ( ; b; b >>= 1, a = (LL)a * a % MOD) if (b & 1) ans = (LL)ans * a % MOD; return ans; } int main() { #ifdef hany01 freopen("agc001e.in", "r", stdin); freopen("agc001e.out", "w", stdout); #endif n = read<int>(); For(i, 1, n) A[i] = read<int>(), B[i] = read<int>(), ++ dp[N - A[i]][N - B[i]]; For(i, 1, M) For(j, 1, M) dp[i][j] = ((dp[i - 1][j] + dp[i][j - 1]) % MOD + dp[i][j]) % MOD; fac[0] = 1; For(i, 1, M * 2) fac[i] = (LL)fac[i - 1] * i % MOD; ifac[M * 2] = Pow(fac[M * 2], MOD - 2); Fordown(i, M * 2, 1) ifac[i - 1] = (LL)ifac[i] * i % MOD; For(i, 1, n) (ans += (dp[N + A[i]][N + B[i]] + MOD - (LL)fac[A[i] * 2 + B[i] * 2] * ifac[A[i] * 2] % MOD * ifac[B[i] * 2] % MOD) % MOD) %= MOD; printf("%lld\n", (LL)ans * ((MOD + 1) / 2) % MOD); return 0; }

codenet

s473392639

p04051

cpp

Accepted

#define _CRT_SECURE_NO_WARNINGS #include <iterator> #include <set> #include <queue> #include <iostream> #include <sstream> #include <stack> #include <deque> #include <map> #include <cmath> #include <memory.h> #include <cstdlib> #include <cstdio> #include <cctype> #include <algorithm> #include <utility> #include <time.h> using namespace std; #define FOR(i,a,b) for(int i=(a);i<(b);++i) #define RFOR(i,b,a) for(int i=(b)-1;i>=(a);--i) #define FILL(A,val) memset(A,val,sizeof(A)) #define ITER(it,a) for(__typeof(a.begin()) it=a.begin();it!=a.end();++it) #define ALL(V) V.begin(),V.end() #define SZ(V) (int)V.size() #define PB push_back #define MP make_pair typedef long long Int; typedef unsigned long long UInt; typedef vector<int> VI; typedef pair<int, int> PII; const double Pi = acos(-1.0); const int INF = 1000000000; const int MOD = 1000000007; pair<int, int> A[200200]; int D[5000][5000]; int F[10000]; int bpow(int a, int b) { int res = 1; while (b) { if (b % 2 == 1) { res = (res * (long long)a) % MOD; } a = (a * (long long)a) % MOD; b /= 2; } return res; } int main() { //freopen("in.txt", "r", stdin); int n; scanf("%d", &n); //n = 200000; int minx, miny, maxx, maxy; minx = INF; miny = INF; maxx = -INF; maxy = -INF; FOR(i, 0, n) { scanf("%d%d", &A[i].first, &A[i].second); //A[i] = MP(rand() % 2000 + 1, rand() % 2000 + 1); D[2000 - A[i].first][2000 - A[i].second]++; // D[2000 + A[i].first][2000 + A[i].second]++; minx = min(minx, 2000 - A[i].first); maxx = max(maxx, 2000 + A[i].first); miny = min(miny, 2000 - A[i].second); maxy = max(maxy, 2000 + A[i].second); } FOR(i, minx, maxx + 1) { FOR(j, miny, maxy + 1) { D[i + 1][j] += D[i][j]; if (D[i + 1][j] >= MOD) D[i + 1][j] -= MOD; D[i][j + 1] += D[i][j]; if (D[i][j + 1] >= MOD) D[i][j + 1] -= MOD; } } int res = 0; FOR(i, 0, n) { res += D[2000 + A[i].first][2000 + A[i].second]; if (res >= MOD) res -= MOD; } F[0] = 1; FOR(i, 1, 8001) { F[i] = (F[i - 1] * (long long)i) % MOD; } FOR(i, 0, n) { long long N = (A[i].first + A[i].second) * 2; long long M = A[i].first * 2; long long K = A[i].second * 2; N = F[N]; M = F[M]; K = F[K]; M = bpow(M, MOD - 2); K = bpow(K, MOD - 2); res -= (((N * M) % MOD)*K) % MOD; if (res < 0) res += MOD; } res = (res * (long long)bpow(2, MOD - 2)) % MOD; cout << res << endl; return 0; }

codenet

s574910778

p04051

cpp

Accepted

#include<bits/stdc++.h> using namespace std; #define rep(i,a,b) for(int i=(a);i<=(b);i++) #define re(i,a,b) for(int i=(a);i<(b);i++) #define repd(i,a,b) for(int i=(a);i>=(b);i--) #define run(a) for(int k=head[a];k;k=e[k].ne) #define clr(a) memset(a,0,sizeof(a)); #define il inline #define sz(a) ((int)a.size()) #define all(a) a.begin(),a.end() #define pb push_back #define w1 first #define w2 second #define adm(a,b,c) {a=a+b;if(a>=c)a-=c;else if(a<0)a+=c;} typedef double db; typedef long long ll;typedef long double ld;typedef unsigned long long ull; typedef pair<ll,ll> pa; const int N=4e3+5,M=1e6+5,INF=1e9,mod=1e9+7; const ll linf=1e18;const double eps=1e-8,pi=acos(-1); il int gmin(int &a,int b){if(a>b)a=b;}il ll gmin(ll &a,ll b){if(a>b)a=b;}il int gmax(int &a,int b){if(a<b)a=b;}il ll gmax(ll &a,ll b){if(a<b)a=b;} il void read(ll&x){ll f=1,t=0;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){t=t*10+ch-'0';ch=getchar();}x=t*f;}il ll read(ll&x,ll&y){read(x);read(y);} il void read(int&x){int f=1,t=0;char ch=getchar();while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}while(ch>='0'&&ch<='9'){t=t*10+ch-'0';ch=getchar();}x=t*f;}il int read(int&x,int&y){read(x);read(y);} il void read(int&a,int&b,int&c){read(a);read(b);read(c);}il void read(ll&a,ll&b,ll&c){read(a);read(b);read(c);} il int read(){int x;read(x);return x;} il ll qpow(ll a,ll b,ll p){ll ret=1;for(;b;b>>=1,a=a*a%p)if(b&1)ret=ret*a%p;return ret;}il ll qpow(ll a,ll b){ll ret=1;for(;b;b>>=1,a=a*a%mod)if(b&1)ret=ret*a%mod;return ret;} il ll qmul(ll a,ll b,ll p){ll ret=0;for(;b;b>>=1,a=(a<<1)%p)if(b&1)adm(ret,a,p);return ret;}il ll qmul(ll a,ll b){ll ret=0;for(;b;b>>=1,a=(a<<1)%mod)if(b&1)adm(ret,a,mod);return ret;} il void judge(){ freopen("data.in","r",stdin); freopen("data.out","w",stdout);} ll fac[M],ifac[M],n; ll f[N][N],x[M],y[M]; il void ad(ll&x,ll y){(x+=y)%=mod;} ll C(ll n,ll m){ if(n<0||m<0||n-m<0)return 0; return fac[n]*ifac[m]%mod*ifac[n-m]%mod; } int main(){ read(n); fac[0]=1;rep(i,1,8000)fac[i]=i*fac[i-1]%mod; ifac[8000]=qpow(fac[8000],mod-2,mod); repd(i,8000-1,0)ifac[i]=ifac[i+1]*(i+1)%mod; rep(i,1,n){read(x[i],y[i]);f[-x[i]+2000][-y[i]+2000]++;} rep(i,0,4000)rep(j,0,4000){ if(i)ad(f[i][j],f[i-1][j]); if(j)ad(f[i][j],f[i][j-1]); }ll res=0; rep(i,1,n){ ad(res,f[x[i]+2000][y[i]+2000]); ad(res,mod-C(x[i]+y[i]+x[i]+y[i],x[i]+x[i])); }cout<<res*qpow(2,mod-2,mod)%mod; }

codenet

s063930586

p04051

cpp

Accepted

/* Arthor : Ender_zzm E-mail zzm_ender_wiggin@outlook.com Blog ender-zzm.enbar.cn */ #include <bits/stdc++.h> using namespace std; inline int Isdigit(char c) { if (c < '0' || c > '9') return 0; return 1; } inline int readint(){ register int x = 0, flag = 1; register char ch; while (!Isdigit(ch = getchar())) if (ch == '-') flag = -1; while (x = x * 10 + (ch & 15), Isdigit(ch = getchar())); return x * flag; } inline long long readlong() { register long long x = 0, flag = 1; register char ch; while (!Isdigit(ch = getchar())) if (ch == '-') flag = -1; while (x = x * 10 + (ch & 15), Isdigit(ch = getchar())); return x * flag; } template <class T> inline void write(T x){ if (x < 0) putchar('-'), x = -x; if(x >= 10) write(x / 10); putchar(x % 10 + '0'); } template<class T> inline bool Chkmax(T& x, const T& y) { return x < y ? x = y, true : false; } template<class T> inline bool Chkmin(T& x, const T& y) { return x > y ? x = y, true : false; } #define For(i, x, y) for (int i = (x); i <= (y); i++) #define Rep(i, x, y) for (int i = (x); i >= (y); i--) #define ri readint #define rl readlong #define int long long const int Mod = 1e9 + 7; const int maxn = 1010100; const int maxm = 5040; int n; int a[maxn], b[maxn]; int dp[maxm][maxm]; int fac[maxn], inv[maxn]; int Pow(int x, int y) { int ans = 1; while (y) { if (y & 1) ans = 1ll * ans * x % Mod; y >>= 1; x = 1ll * x * x % Mod; } return ans; } long long C(int n, int m) { int tmp = 1ll * fac[m] * fac[n - m] % Mod; tmp = Pow(tmp, Mod - 2); return 1ll * tmp * fac[n] % Mod; } signed main() { n = ri(); int K = 2010; fac[0] = 1; for (int i = 1; i <= 4 * K; i++) { fac[i] = 1ll * fac[i - 1] * i % Mod; } inv[4 * K] = Pow(fac[4 * K], Mod - 2); for (int i = 4 * K - 1; i >= 0; i--) { inv[i] = 1ll * inv[i + 1] * (i + 1) % Mod; } for (int i = 1; i <= n; i++) { a[i] = ri(), b[i] = ri(); dp[-1 * a[i] + K][-1 * b[i] + K] += 1; } for (int i = 0; i <= 2 * K; i++) { for (int j = 0; j <= 2 * K; j++) { if (i - 1 >= 0) dp[i][j] = (dp[i][j] + dp[i - 1][j]) % Mod; if (j - 1 >= 0) dp[i][j] = (dp[i][j] + dp[i][j - 1]) % Mod; } } int ans = 0; for (int i = 1; i <= n; i++) { (ans += dp[a[i] + K][b[i] + K]) %= Mod; } for (int i = 1; i <= n; i++) { ans = (ans - C(2 * a[i] + 2 * b[i], 2 * a[i]) + Mod) % Mod; } ans = 1ll * ans * Pow(2, Mod - 2) % Mod; printf("%lld\n", ans); return 0; }

codenet

s063930586

p04051

cpp

Accepted

/* Arthor : Ender_zzm E-mail zzm_ender_wiggin@outlook.com Blog ender-zzm.enbar.cn */ #include <bits/stdc++.h> using namespace std; inline int Isdigit(char c) { if (c < '0' || c > '9') return 0; return 1; } inline int readint(){ register int x = 0, flag = 1; register char ch; while (!Isdigit(ch = getchar())) if (ch == '-') flag = -1; while (x = x * 10 + (ch & 15), Isdigit(ch = getchar())); return x * flag; } inline long long readlong() { register long long x = 0, flag = 1; register char ch; while (!Isdigit(ch = getchar())) if (ch == '-') flag = -1; while (x = x * 10 + (ch & 15), Isdigit(ch = getchar())); return x * flag; } template <class T> inline void write(T x){ if (x < 0) putchar('-'), x = -x; if(x >= 10) write(x / 10); putchar(x % 10 + '0'); } template<class T> inline bool Chkmax(T& x, const T& y) { return x < y ? x = y, true : false; } template<class T> inline bool Chkmin(T& x, const T& y) { return x > y ? x = y, true : false; } #define For(i, x, y) for (int i = (x); i <= (y); i++) #define Rep(i, x, y) for (int i = (x); i >= (y); i--) #define ri readint #define rl readlong #define int long long const int Mod = 1e9 + 7; const int maxn = 1010100; const int maxm = 5040; int n; int a[maxn], b[maxn]; int dp[maxm][maxm]; int fac[maxn], inv[maxn]; int Pow(int x, int y) { int ans = 1; while (y) { if (y & 1) ans = 1ll * ans * x % Mod; y >>= 1; x = 1ll * x * x % Mod; } return ans; } long long C(int n, int m) { int tmp = 1ll * fac[m] * fac[n - m] % Mod; tmp = Pow(tmp, Mod - 2); return 1ll * tmp * fac[n] % Mod; } signed main() { n = ri(); int K = 2010; fac[0] = 1; for (int i = 1; i <= 4 * K; i++) { fac[i] = 1ll * fac[i - 1] * i % Mod; } inv[4 * K] = Pow(fac[4 * K], Mod - 2); for (int i = 4 * K - 1; i >= 0; i--) { inv[i] = 1ll * inv[i + 1] * (i + 1) % Mod; } for (int i = 1; i <= n; i++) { a[i] = ri(), b[i] = ri(); dp[-1 * a[i] + K][-1 * b[i] + K] += 1; } for (int i = 0; i <= 2 * K; i++) { for (int j = 0; j <= 2 * K; j++) { if (i - 1 >= 0) dp[i][j] = (dp[i][j] + dp[i - 1][j]) % Mod; if (j - 1 >= 0) dp[i][j] = (dp[i][j] + dp[i][j - 1]) % Mod; } } int ans = 0; for (int i = 1; i <= n; i++) { (ans += dp[a[i] + K][b[i] + K]) %= Mod; } for (int i = 1; i <= n; i++) { ans = (ans - C(2 * a[i] + 2 * b[i], 2 * a[i]) + Mod) % Mod; } ans = 1ll * ans * Pow(2, Mod - 2) % Mod; printf("%lld\n", ans); return 0; }

codenet

s471544577

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #ifdef Lin1043 #define DEBUG(msg, ...) printf("(%s #%d) " msg, __FUNCTION__, __LINE__, __VA_ARGS__) #define massert(...) assert(...) #else #define DEBUG(...) #define massert(...) #endif #define rep(i , l , r) for(int i = (l) , ___ = (r) ; i <= ___ ; ++i ) #define per(i , r , l) for(int i = (r) , ___ = (l) ; i >= ___ ; --i ) struct iopener { iopener() { #ifdef Lin1043 freopen("./in" , "r" , stdin); #endif } } iop; typedef long long LL; template<typename T>inline bool chkmin(T &x , const T &y) { return x > y ? (x = y , 1) : 0; } template<typename T>inline bool chkmax(T &x , const T &y) { return x < y ? (x = y , 1) : 0; } template<typename T>inline T read(T &f) { f = 0; int x = 1 ; char c = getchar(); while(!isdigit(c)) x = (c == '-' ? -1 : 1) , c = getchar(); while(isdigit(c)) (f *= 10) += c & 15 , c = getchar(); return f = x * f; } const int N = 200000 + 5; const int KCZ = 1e9 + 7 , L = N - 5; int n , A[N] , B[N]; LL fac[N] , inv[N]; LL mp(LL x , LL y = KCZ - 2) { LL res = 1; while(y) { if(y & 1) res = res * x % KCZ; x = x * x % KCZ; y >>= 1; } return res; } void init() { fac[0] = 1; rep(i , 1 , L) fac[i] = fac[i - 1] * i % KCZ; inv[0] = 1; inv[L] = mp(fac[L]); per(i , L - 1 , 1) inv[i] = inv[i + 1] * (i + 1) % KCZ; } int delta; const int M = 4000 + 5; LL f[M][M]; void add(LL &x , const LL &y) { x += y ; if(x >= KCZ) x -= KCZ; } void sub(LL &x , const LL &y) { x -= y ; if(x < 0) x += KCZ; } LL C(int n , int m) { if(n < m) return 0; return fac[n] * inv[m] % KCZ * inv[n - m] % KCZ; } int main() { read(n) , init(); rep(i , 1 , n) read(A[i]) , read(B[i]); rep(i , 1 , n) chkmax(delta , max(A[i] , B[i])); rep(i , 1 , n) f[delta - A[i]][delta - B[i]]++; rep(i , -delta , delta) rep(j , -delta , delta) { if(i >= -delta + 1) add(f[i + delta][j + delta] , f[i - 1 + delta][j + delta]); if(j >= -delta + 1) add(f[i + delta][j + delta] , f[i + delta][j - 1 + delta]); } LL Ans = 0; rep(i , 1 , n) { add(Ans , f[delta + A[i]][delta + B[i]]); sub(Ans , C(2 * (A[i] + B[i]) , 2 * A[i])); } Ans = Ans * mp(2) % KCZ; cout << Ans << endl; return 0; }

codenet

s219188766

p04051

cpp

Accepted

/* О НЕТ! ОНИ ДОГОНЯЮТ!!! 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 🐹🐹🐹🐹🐹🐹🐹🐹🐹🐹 */ #include <cmath> #include <iostream> #include <vector> #include <algorithm> #include <string> #include <set> #include <map> #include <list> #include <time.h> #include <math.h> #include <random> #include <deque> #include <queue> #include <cassert> #include <unordered_map> #include <iomanip> using namespace std; typedef long long ll; mt19937 rnd(228); const int N = 2e5 + 7; const int M = 5000 + 1; const int MOD = 1e9 + 7; const int ADD = 2000; int a[M][M], b[M][M]; int x[N], y[N]; int dp[M][M]; int cnt[M][M]; int fact[N]; int rev[N]; inline int add(int a, int b) { return (a + b >= MOD ? a + b - MOD : a + b < 0 ? a + b + MOD : a + b); } inline int mul(int a, int b) { return (a * (ll) b) % MOD; } int bin(int a, int n) { int res = 1; while (n) { if (n % 2 == 0) { a = mul(a, a); n /= 2; } else { res = mul(res, a); n--; } } return res; } int C(int n, int k) { return mul(fact[n], mul(rev[n - k], rev[k])); } int main() { #ifdef ONPC freopen("a.in", "r", stdin); #endif fact[0] = 1; for (int i = 1; i < N; i++) { fact[i] = mul(fact[i - 1], i); } /* rev[N - 1] = mul(fact[N - 1], MOD - 2); for (int i = N - 2; i >= 0; i--) { rev[i] = mul(rev[i + 1], i + 1); } */ for (int i = 0; i < N; i++) { rev[i] = bin(fact[i], MOD - 2); } int n; scanf("%d", &n); for (int i = 0; i < n; i++) { scanf("%d%d", &x[i], &y[i]); a[-x[i] + ADD][-y[i] + ADD]++; b[x[i] + ADD][y[i] + ADD]++; } for (int i = 0; i + 1 < M; i++) { for (int j = 0; j + 1 < M; j++) { dp[i][j] = add(dp[i][j], a[i][j]); dp[i + 1][j] = add(dp[i + 1][j], dp[i][j]); dp[i][j + 1] = add(dp[i][j + 1], dp[i][j]); } } int ans = 0; for (int i = 0; i < M; i++) { for (int j = 0; j < M; j++) { ans = add(ans, mul(b[i][j], dp[i][j])); } } for (int i = 0; i < n; i++) { int get = C(x[i] + x[i] + y[i] + y[i], x[i] + x[i]); ans = add(ans, -get); } ans = mul(ans, rev[2]); printf("%d\n", ans); }

codenet

s185792908

p04051

cpp

Accepted

#include <bits/stdc++.h> #define IL __inline__ __attribute__((always_inline)) #define For(i, a, b) for (int i = a, i##end = b; i <= i##end; ++ i) #define FOR(i, a, b) for (int i = a, i##end = b; i < i##end; ++ i) #define Rep(i, a, b) for (int i = a, i##end = b; i >= i##end; -- i) #define REP(i, a, b) for (int i = (a) - 1, i##end = b; i >= i##end; -- i) typedef long long LL; template <class T> IL bool chkmax(T &a, const T &b) { return a < b ? ((a = b), 1) : 0; } template <class T> IL bool chkmin(T &a, const T &b) { return a > b ? ((a = b), 1) : 0; } template <class T> IL T mymax(const T &a, const T &b) { return a > b ? a : b; } template <class T> IL T mymin(const T &a, const T &b) { return a < b ? a : b; } template <class T> IL T myabs(const T &a) { return a > 0 ? a : -a; } const int INF = 0X3F3F3F3F; const double EPS = 1E-10, PI = acos(-1.0); #define DEBUG(...) fprintf(stderr, __VA_ARGS__) #define OK DEBUG("Passing [%s] in LINE %d...\n", __FUNCTION__, __LINE__) /*------------------------------header------------------------------*/ const int MAXN = 200000 + 5, MAXM = 2000 + 5, MOD = 1000000007, INV_2 = 500000004; IL int add(int a, int b) { a += b; return a >= MOD ? a - MOD : a; } IL int sub(int a, int b) { a -= b; return a < 0 ? a + MOD : a; } IL int mul(int a, int b) { return 1LL * a * b % MOD; } IL int pow_mod(int a, int p) { int result = 1; for (int base = a; p; p >>= 1, base = mul(base, base)) { if (p & 1) { result = mul(result, base); } } return result; } int a[MAXN], b[MAXN], f[MAXM * 2][MAXM * 2], fac[MAXN * 4], ifac[MAXN * 4]; IL void Init(int n) { fac[0] = 1; For(i, 1, n) { fac[i] = mul(fac[i - 1], i); } ifac[n] = pow_mod(fac[n], MOD - 2); REP(i, n, 0) { ifac[i] = mul(ifac[i + 1], i + 1); } } IL int C(int n, int m) { return mul(fac[n], mul(ifac[m], ifac[n - m])); } int main() { int n; scanf("%d", &n); int max_a = 0, max_b = 0; For(i, 1, n) { scanf("%d%d", &a[i], &b[i]); ++ f[MAXM - a[i]][MAXM - b[i]]; chkmax(max_a, a[i]); chkmax(max_b, b[i]); } For(i, MAXM - max_a, MAXM + max_a) { For(j, MAXM - max_b, MAXM + max_b) { f[i][j] = add(f[i][j], add(f[i][j - 1], f[i - 1][j])); } } Init(max_a * 2 + max_b * 2); int ans = 0; For(i, 1, n) { ans = add(ans, f[MAXM + a[i]][MAXM + b[i]]); ans = sub(ans, C((a[i] + b[i]) << 1, a[i] << 1)); } printf("%d\n", mul(ans, INV_2)); return 0; }

codenet

s909813276

p04051

cpp

Accepted

#include <bits/stdc++.h> #define INF 2000000000 #define MOD 1000000007 #define MAXN 200005 #define REP(temp, init_val, end_val) for (int temp = init_val; temp <= end_val; ++temp) #define REPR(temp, init_val, end_val) for (int temp = init_val; temp >= end_val; --temp) using namespace std; typedef long long ll; typedef unsigned long long ull; typedef pair<int, int> intpair; int read(){ int f = 1, x = 0; char c = getchar(); while (c < '0' || c > '9'){if(c == '-') f = -f; c = getchar();} while (c >= '0' && c <= '9')x = x * 10 + c - '0', c = getchar(); return f * x; } inline int lowbit(int x){ return x & (-x); } inline int modadd(int x, int y){ return (x + y >= MOD ? x + y - MOD: x + y); } inline int sgn(int x){ return (x < 0 ? -1: (x > 0 ? 1: 0)); } template<typename T> T gcd(T a, T b){ return (!b) ? a: gcd(b, a % b); } int poww(int a, int b){ int res = 1; while (b > 0){ if (b & 1) res = 1ll * res * a % MOD; a = 1ll * a * a % MOD, b >>= 1; } return res; } const int dx[] = {-1, 0, 1, 0}, dy[] = {0, 1, 0, -1}; const int ddx[] = {-1, -1, -1, 0, 0, 1, 1, 1}, ddy[] = {-1, 0, 1, -1, 1, -1, 0, 1}; /*--------------------------------------------------------------------*/ /*--------------------------------------------------------------------*/ const int inv2 = 1000000008 / 2; const int offset = 2001; int fac[8005], inv[8005], invfac[8005]; int n, a[200005], b[200005]; int f[4005][4005] = {0}; void init(){ n = read(); for (int i = 1; i <= n; ++i) a[i] = read(), b[i] = read(), ++f[-a[i] + offset][-b[i] + offset]; fac[0] = fac[1] = 1; inv[1] = 1; invfac[0] = invfac[1] = 1; for (int i = 2; i <= 8000; ++i){ fac[i] = 1ll * fac[i - 1] * i % MOD; inv[i] = 1ll * (MOD - MOD / i) * inv[MOD % i] % MOD; invfac[i] = 1ll * invfac[i - 1] * inv[i] % MOD; } } void solve(){ for (int i = 1; i <= 4001; ++i) for (int j = 1; j <= 4001; ++j){ f[i][j] = modadd(f[i - 1][j], modadd(f[i][j], f[i][j - 1])); } int ans = 0; for (int i = 1; i <= n; ++i){ ans = modadd(ans, f[a[i] + offset][b[i] + offset]); int cc = 1ll * fac[2 * a[i] + 2 * b[i]] * invfac[2 * a[i]] % MOD; cc = 1ll * cc * invfac[2 * b[i]] % MOD; ans = modadd(ans, MOD - cc); } ans = 1ll * ans * inv2 % MOD; printf("%d\n", ans); } int main(){ int T = 1; while (T--){ init(); solve(); } return 0; }

codenet

s569160588

p04051

cpp

Accepted

#define DEBUG 0 #include <bits/stdc++.h> using namespace std; #if DEBUG // basic debugging macros int __i__,__j__; #define printLine(l) for(__i__=0;__i__<l;__i__++){cout<<"-";}cout<<endl #define printLine2(l,c) for(__i__=0;__i__<l;__i__++){cout<<c;}cout<<endl #define printVar(n) cout<<#n<<": "<<n<<endl #define printArr(a,l) cout<<#a<<": ";for(__i__=0;__i__<l;__i__++){cout<<a[__i__]<<" ";}cout<<endl #define print2dArr(a,r,c) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<a[__i__][__j__]<<" ";}cout<<endl;} #define print2dArr2(a,r,c,l) cout<<#a<<":\n";for(__i__=0;__i__<r;__i__++){for(__j__=0;__j__<c;__j__++){cout<<setw(l)<<setfill(' ')<<a[__i__][__j__]<<" ";}cout<<endl;} // advanced debugging class // debug 1,2,'A',"test"; class _Debug { public: template<typename T> _Debug& operator,(T val) { cout << val << endl; return *this; } }; #define debug _Debug(), #else #define printLine(l) #define printLine2(l,c) #define printVar(n) #define printArr(a,l) #define print2dArr(a,r,c) #define print2dArr2(a,r,c,l) #define debug #endif // define #define MAX_VAL 999999999 #define MAX_VAL_2 999999999999999999LL #define EPS 1e-6 #define mp make_pair #define pb push_back // typedef typedef unsigned int UI; typedef long long int LLI; typedef unsigned long long int ULLI; typedef unsigned short int US; typedef pair<int,int> pii; typedef pair<LLI,LLI> plli; typedef vector<int> vi; typedef vector<LLI> vlli; typedef vector<pii> vpii; typedef vector<plli> vplli; // ---------- END OF TEMPLATE ---------- #define MOD 1000000007 int A[200000],B[200000]; int fact[8001]; int dp[4002][4002]; int inv(LLI n) { LLI r = 1; int e = MOD-2; while (e > 0) { if (e & 1) r *= n,r %= MOD; e >>= 1; n *= n,n %= MOD; } return r; } int main() { int i; int N; scanf("%d",&N); for (i = 0; i < N; i++) scanf("%d %d",&A[i],&B[i]),dp[2001-A[i]][2001-B[i]]++; int j; for (i = 1; i < 4002; i++) { for (j = 1; j < 4002; j++) dp[i][j] += dp[i-1][j]+dp[i][j-1],dp[i][j] %= MOD; } fact[0] = 1; for (i = 1; i <= 8000; i++) fact[i] = ((LLI) fact[i-1]*i) % MOD; int ans = 0; for (i = 0; i < N; i++) { ans += dp[A[i]+2001][B[i]+2001],ans %= MOD; ans -= ((LLI) fact[2*A[i]+2*B[i]]*inv(((LLI) fact[2*A[i]]*fact[2*B[i]]) % MOD)) % MOD,ans %= MOD; } if (ans < 0) ans += MOD; printf("%lld\n",((LLI) ans*inv(2)) % MOD); return 0; }

codenet

s836727463

p04051

cpp

Accepted

#include <iostream> #include <cstdio> #include <cassert> #include <cstring> #include <vector> #include <valarray> #include <array> #include <queue> #include <set> #include <unordered_set> #include <map> #include <unordered_map> #include <algorithm> #include <cmath> #include <complex> #include <random> using namespace std; using ll = long long; using ull = unsigned long long; constexpr int TEN(int n) {return (n==0)?1:10*TEN(n-1);} template<class T> T pow(T x, ll n) { T r = 1; while (n) { if (n & 1) r *= x; x *= x; n >>= 1; } return r; } template<uint MD> struct ModInt { uint v; ModInt() : v(0) {} ModInt(ll v) : v(normS(v%MD+MD)) {} uint value() const {return v;} static uint normS(const uint &x) {return (x<MD)?x:x-MD;}; static ModInt make(const uint &x) {ModInt m; m.v = x; return m;} const ModInt operator+(const ModInt &r) const {return make(normS(v+r.v));} const ModInt operator-(const ModInt &r) const {return make(normS(v+normS(MD-r.v)));} const ModInt operator*(const ModInt &r) const {return make((ull)v*r.v%MD);} ModInt& operator+=(const ModInt &r) {return *this=*this+r;} ModInt& operator-=(const ModInt &r) {return *this=*this-r;} ModInt& operator*=(const ModInt &r) {return *this=*this*r;} static ModInt inv(const ModInt &x) { return pow(ModInt(x), MD-2); } }; using Mint = ModInt<TEN(9)+7>; const int MN = 4040; Mint g[MN][MN]; Mint C[MN][MN]; Mint fact[2*MN], iFac[2*MN]; void first() { fact[0] = 1; for (int i = 1; i < 2*MN; i++) { fact[i] = fact[i-1]*i; } for (int i = 0; i < 2*MN; i++) { iFac[i] = Mint::inv(fact[i]); } C[0][0] = 1; for (int i = 1; i < MN; i++) { C[i][0] = C[i-1][0]; for (int j = 1; j < MN; j++) { C[i][j] = C[i-1][j]+C[i-1][j-1]; } } } int main() { first(); int m; cin >> m; int a[m], b[m]; for (int i = 0; i < m; i++) { cin >> a[i] >> b[i]; } Mint off = 0; for (int i = 0; i < m; i++) { // off += C[2*a[i]+2*b[i]][2*b[i]]; off += fact[2*a[i]+2*b[i]]*iFac[2*a[i]]*iFac[2*b[i]]; } for (int i = 0; i < m; i++) { g[2010-a[i]][2010-b[i]] += 1; } for (int i = 1; i < MN; i++) { for (int j = 1; j < MN; j++) { g[i][j] += g[i-1][j]+g[i][j-1]; } } Mint ans = 0; for (int i = 0; i < m; i++) { ans += g[2010+a[i]][2010+b[i]]; } ans -= off; ans *= Mint::inv(2); cout << ans.value() << endl; return 0; }

codenet

s131640242

p04051

cpp

Accepted

#include <algorithm> #include <bitset> #include <complex> #include <deque> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <queue> #include <set> #include <stack> #include <string> #include <vector> #include <random> #include <tuple> #include <iomanip> #include <cstring> using namespace std; typedef long long ll; //typedef pair<int,int> Pint; //typedef pair<ll, ll> P; //typedef pair<ll, pair<ll, ll>> P; //typedef tuple<int,int,int> T; typedef vector<ll> vec; typedef vector<vec> mat; #define rep(i, n) for(ll i = 0; i < (n); i++) #define revrep(i, n) for(ll i = (n-1); i >= 0; i--) #define pb push_back #define f first #define s second const ll INFL = 1LL << 60;//10^18 = 2^60 const int INF = 1 << 30;//10^9 ll MOD = 1e9 + 7; //ll MOD = 998244353; vector<ll> dy = {0, 0, 1, -1, 1, 1, -1, -1, 0}; vector<ll> dx = {1, -1, 0, 0, 1, -1, 1, -1, 0}; ll max(ll a, ll b){return (a > b) ? a : b;} ll min(ll a, ll b){return (a < b) ? a : b;} ll pow_long(ll x, ll k){ ll res = 1; while(k > 0){ if(k % 2) res *= x; x *= x; k /= 2; } return res; } ll pow_mod(ll x, ll k){ x %= MOD; x += MOD; x %= MOD; ll res = 1; while(k > 0){ if(k % 2){ res *= x; res %= MOD; } x *= x; x %= MOD; k /= 2; } return res; } ll inverse(ll x){return pow_mod(x, MOD - 2);}; //最大公約数 ll gcd(ll a, ll b){ if(b == 0) return a; return gcd(b, a % b); } //最小公倍数 ll lcm(ll x, ll y){return x / gcd(x, y) * y;}; //コンビネーション const int MAXcomb = 200010; ll fac[MAXcomb], finv[MAXcomb], inv[MAXcomb]; //facはn!,finvは1/n! //invは逆元 void COMinit(){ fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i = 2; i < MAXcomb; i++){ fac[i] = fac[i-1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD; finv[i] = finv[i-1] * inv[i] % MOD; } } ll comb(int n, int k){ if(n < k) return 0; if(n < 0 || k < 0) return 0; return fac[n] * finv[k] % MOD * finv[n-k] % MOD; } ll dp[4010][4010]; int main(void){ COMinit(); ll N; cin >> N; vector<ll> A(N), B(N); rep(i, N) cin >> A[i] >> B[i]; rep(i, N){ dp[2000-A[i]][2000-B[i]]++; } rep(i, 4005)rep(j, 4005){ dp[i+1][j] += dp[i][j]; dp[i][j+1] += dp[i][j]; dp[i+1][j] %= MOD; dp[i][j+1] %= MOD; } ll ans = 0; rep(i, N){ ans += dp[2000+A[i]][2000+B[i]]; ans %= MOD; } rep(i, N){ ans -= comb(2*A[i]+2*B[i], 2*A[i]); ans %= MOD; } ans += MOD; ans %= MOD; ans *= inverse(2); ans %= MOD; cout << ans << endl; }

codenet

s131640242

p04051

cpp

Accepted

#include <algorithm> #include <bitset> #include <complex> #include <deque> #include <iostream> #include <istream> #include <iterator> #include <limits> #include <list> #include <map> #include <memory> #include <queue> #include <set> #include <stack> #include <string> #include <vector> #include <random> #include <tuple> #include <iomanip> #include <cstring> using namespace std; typedef long long ll; //typedef pair<int,int> Pint; //typedef pair<ll, ll> P; //typedef pair<ll, pair<ll, ll>> P; //typedef tuple<int,int,int> T; typedef vector<ll> vec; typedef vector<vec> mat; #define rep(i, n) for(ll i = 0; i < (n); i++) #define revrep(i, n) for(ll i = (n-1); i >= 0; i--) #define pb push_back #define f first #define s second const ll INFL = 1LL << 60;//10^18 = 2^60 const int INF = 1 << 30;//10^9 ll MOD = 1e9 + 7; //ll MOD = 998244353; vector<ll> dy = {0, 0, 1, -1, 1, 1, -1, -1, 0}; vector<ll> dx = {1, -1, 0, 0, 1, -1, 1, -1, 0}; ll max(ll a, ll b){return (a > b) ? a : b;} ll min(ll a, ll b){return (a < b) ? a : b;} ll pow_long(ll x, ll k){ ll res = 1; while(k > 0){ if(k % 2) res *= x; x *= x; k /= 2; } return res; } ll pow_mod(ll x, ll k){ x %= MOD; x += MOD; x %= MOD; ll res = 1; while(k > 0){ if(k % 2){ res *= x; res %= MOD; } x *= x; x %= MOD; k /= 2; } return res; } ll inverse(ll x){return pow_mod(x, MOD - 2);}; //最大公約数 ll gcd(ll a, ll b){ if(b == 0) return a; return gcd(b, a % b); } //最小公倍数 ll lcm(ll x, ll y){return x / gcd(x, y) * y;}; //コンビネーション const int MAXcomb = 200010; ll fac[MAXcomb], finv[MAXcomb], inv[MAXcomb]; //facはn!,finvは1/n! //invは逆元 void COMinit(){ fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for(int i = 2; i < MAXcomb; i++){ fac[i] = fac[i-1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD; finv[i] = finv[i-1] * inv[i] % MOD; } } ll comb(int n, int k){ if(n < k) return 0; if(n < 0 || k < 0) return 0; return fac[n] * finv[k] % MOD * finv[n-k] % MOD; } ll dp[4010][4010]; int main(void){ COMinit(); ll N; cin >> N; vector<ll> A(N), B(N); rep(i, N) cin >> A[i] >> B[i]; rep(i, N){ dp[2000-A[i]][2000-B[i]]++; } rep(i, 4005)rep(j, 4005){ dp[i+1][j] += dp[i][j]; dp[i][j+1] += dp[i][j]; dp[i+1][j] %= MOD; dp[i][j+1] %= MOD; } ll ans = 0; rep(i, N){ ans += dp[2000+A[i]][2000+B[i]]; ans %= MOD; } rep(i, N){ ans -= comb(2*A[i]+2*B[i], 2*A[i]); ans %= MOD; } ans += MOD; ans %= MOD; ans *= inverse(2); ans %= MOD; cout << ans << endl; }

codenet

s168290962

p04051

cpp

Accepted

#include <iostream> #include <vector> #include <algorithm> #include <cmath> #include <string> #include <queue> #include <stack> #include <set> #include <map> #include <iomanip> #include <utility> #include <tuple> #include <functional> #include <bitset> #include <cassert> #include <complex> #include <time.h> #define int long long #define endl '\n' #define INF 1000000000000000000 #define EPS 1e-10 #define PI 3.141592653589793238 #define all(a) a.begin(),a.end() #define rep(i, n) for (int i = 0; i < (n); i++) #define pb push_back #define double long double using namespace std; typedef long long ll; typedef pair<ll, ll> P; typedef pair<ll, P> PP; typedef complex<double> com; template<class T, class S> bool chmax(T &a, const S &b) { if (a < b) { a = b; return 1; } return 0; } template<class T, class S> bool chmin(T &a, const S &b) { if (a > b) { a = b; return 1; } return 0; } ll gcd(ll n, ll m) { return (m ? gcd(m, n%m) : n); } ll lcm(ll n, ll m) { return n / gcd(n, m)*m; } ll mod = 1000000007; ll modsize = 10000; ll modinv(ll a) { ll b = mod, u = 1, v = 0; while (b) { ll t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } u %= mod; if (u < 0) u += mod; return u; } ll modpow(ll a, ll b) { ll ans = 1; a %= mod; while (b) { if (b & 1) ans = ans * a%mod; a = a * a%mod; b >>= 1; } return ans; } vector<ll> fac(modsize + 5); vector<ll> inv(modsize + 5); vector<ll> facinv(modsize + 5); void modcalc() { fac[0] = fac[1] = 1; inv[1] = 1; facinv[0] = facinv[1] = 1; for (int i = 2; i < modsize; i++) { fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod%i] * (mod / i) % mod; facinv[i] = facinv[i - 1] * inv[i] % mod; } } ll modcomb(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[k] % mod * facinv[n - k] % mod; } ll modperm(ll n, ll k) { if (n < 0 || k < 0 || n < k) return 0; return fac[n] * facinv[n - k] % mod; } ll modhom(ll n, ll k) { if (n < 0 || k < 0) return 0; if (n == 0 && k == 0) return 1; return modcomb(n + k - 1, k); } int dp[4020][4020]; signed main() { cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); modcalc(); int n; cin >> n; vector<int> a(n), b(n); rep(i, n) { cin >> a[i] >> b[i]; dp[2002 - a[i]][2002 - b[i]]++; } rep(i, 4010) { rep(j, 4010) { dp[i + 1][j + 1] += dp[i + 1][j]; dp[i + 1][j + 1] += dp[i][j + 1]; dp[i + 1][j + 1] %= mod; } } int ans = 0; rep(i, n) { ans += dp[2002 + a[i]][2002 + b[i]]; ans -= modcomb(2 * (a[i] + b[i]), 2 * a[i]); ans += mod; } cout << ans % mod * inv[2] % mod << endl; }

codenet

s202707976

p04051

cpp

Accepted

/*{{{*/ //#pragma GCC optimize("O3") #include <bits/stdc++.h> #ifdef __linux__ #define getchar getchar_unlocked #define putchar putchar_unlocked #endif typedef long long ll; typedef std::pair<int, int> pii; std::string Name = __FILE__; std::string iput = Name.substr(0, Name.length() - 4) + ".in"; std::string oput = Name.substr(0, Name.length() - 4) + ".out"; template <class T> inline bool chkmin(T &x, T y) { return x > y ? x = y, true : false; } template <class T> inline bool chkmax(T &x, T y) { return x < y ? x = y, true : false; } template <class T> inline T &read(T &x) { static int f; static char c; for (f = 1; !isdigit(c = getchar()); ) { if (c == '-') f = -1; } for (x = 0; isdigit(c); c = getchar()) { x = x * 10 + c - 48; } return x *= f; } template <class T> inline void write(T x, const char p = '\n') { static int top; static int s[30]; if (x < 0) { x = -x; putchar('-'); } do s[++ top] = x % 10 + 48; while (x /= 10); while (top) putchar(s[top --]); putchar(p); } /*}}}*/ const int maxn = 2e5 + 5; const int maxm = 2000 + 5; const int mo = 1e9 + 7; const int inv2 = mo + 1 >> 1; int n; int m; int a[maxn], b[maxn]; int c[maxm << 1][maxm << 1]; long long fac[maxn << 2], inv[maxn << 2]; int C(int a, int b) { return (long long)fac[a] * inv[b] % mo * inv[a - b] % mo; } int qpow(int a, int b) { int ret = 1; while (b) { if (b & 1) ret = (long long)ret * a % mo; a = (long long)a * a % mo; b >>= 1; } return ret; } void exec() { for (int i = fac[0] = 1; i <= 8000; ++ i) { fac[i] = (long long)fac[i - 1] * i % mo; } inv[8000] = qpow(fac[8000], mo - 2); for (int i = 8000 - 1; ~i; -- i) { inv[i] = (long long)inv[i + 1] * (i + 1) % mo; } read(n); for (int i = 1; i <= n; ++ i) { read(a[i]), read(b[i]); ++ c[maxm - a[i]][maxm - b[i]]; } for (int i = 1; i < maxm << 1; ++ i) for (int j = 1; j < maxm << 1; ++ j) (c[i][j] += (c[i - 1][j] + c[i][j - 1]) % mo) %= mo; int ans = 0; for (int i = 1; i <= n; ++ i) { (ans += c[maxm + a[i]][maxm + b[i]]) %= mo; (ans += mo - C(a[i] + b[i] << 1, a[i] << 1)) %= mo; } write((long long)ans * inv2 % mo); } /*{{{*/ int main() { if (fopen(iput.c_str(), "r") != NULL) { freopen(iput.c_str(), "r", stdin); freopen(oput.c_str(), "w", stdout); } exec(); fclose(stdin); fclose(stdout); return 0; } /*}}}*/

codenet

s799752264

p04051

cpp

Accepted

#include<bits/stdc++.h> #include<cmath> using namespace std; typedef long long ll; typedef unsigned long long ull; typedef vector<int> vi; typedef pair<int,int> pii; const int inf = 0x3f3f3f3f,oo = inf; #define pi 3.14159265358979323846 #define IL inline #define RG register #define rep(i,a,b) for(RG int i=(a);i<(b);++i) #define Rep(i,a,b) for(RG int i=(a);i<=(b);++i) #define Dep(i,a,b) for(RG int i=(a);i>=(b);--i) #define pc putchar /*char __wzp[1<<15|1],*__S=__wzp+32768; #define gc() (__S>=__wzp+32768?(__wzp[fread(__wzp,sizeof(char),1<<15,stdin)]=EOF),*((__S=__wzp)++):*(__S++))*/ #define gc getchar IL ll read(){ RG ll x=0;char f=0;RG char c=gc(); for(;!isdigit(c);c=gc())f|=(c=='-'); for(;isdigit(c);c=gc())x=(x<<1)+(x<<3)+(c^48); return f?-x:x; } IL double readdb(){ RG double x=0,p=0.1;RG char f=0,c=gc(); for(;!isdigit(c);c=gc())f|=(c=='-'); for(;isdigit(c);c=gc())x=x*10+(c^48); if(c=='.')for(c=gc();isdigit(c);c=gc(),p/=10)x=x+(c^48)*p; return f?-x:x; } IL void write(ll x){if(x<0)x=-x,pc('-');if(x>=10)write(x/10);pc(x%10+'0');} IL void writeln(ll x){write(x);puts("");} IL void writeln(ll x,char c,ll y){write(x);pc(c);writeln(y);} IL void writeln(ll x,char c,ll y,char d,ll z){write(x);pc(c);write(y);pc(d);writeln(z);} #define debug(x) printf(#x" = %d\n",x); #define rd() read() #define rdb() readdb() #define mem(x,v) memset(x,v,sizeof(x)) #define pb push_back #define mp make_pair #define sqr(x) ((x)*(x)) #define lowbit(x) ((x)&(-(x))) #define fin(x) freopen(#x".in","r",stdin) #define fout(x) freopen(#x".out","w",stdout) #define y1 ____y1 #define hash __hash #define union _union const int Mod =1e9+7; const int maxn = 205050; int n,A[maxn],B[maxn],f[4005][4005]; int fac[8005],inv[8005]; int C(int n,int m){ // printf("(%d %d) = %d\n",n,m,1ll * fac[n] * inv[m] % Mod * inv[n-m] % Mod); return 1ll * fac[n] * inv[m] % Mod * inv[n-m] % Mod; } int qpow(int a,int b){ int ans = 1; for(;b;b>>=1,a=1ll*a*a%Mod){ if(b&1) ans = 1ll*ans*a%Mod; }return ans; } int main(){ n = rd(); fac[0] = 1; Rep(i,1,8001) fac[i] = 1ll * fac[i-1] * i % Mod; inv[8001] = qpow(fac[8001],Mod-2); Dep(i,8000,0) inv[i] = 1ll * inv[i+1] * (i+1) % Mod; Rep(i,1,n){ A[i] = rd(),B[i] = rd(); f[-A[i]+2000][-B[i]+2000]++; } for(int i=0;i<=4000;i++) for(int j=0;j<=4000;j++){ if(j) f[i][j] = (f[i][j] + f[i][j-1]) % Mod; if(i) f[i][j] = (f[i][j] + f[i-1][j]) % Mod; } int ans = 0; Rep(i,1,n){ ans = (ans + f[A[i]+2000][B[i]+2000]) % Mod; ans = (ans - C(A[i]+A[i]+B[i]+B[i],A[i]+A[i]) + Mod) % Mod; } writeln(1ll*ans*inv[2]%Mod); return 0; }

codenet

s473657856

p04051

cpp

Accepted

#include <bits/stdc++.h> #include <string> using namespace std; /******************************************* ****************** BY ********************** ******* FUTURE GOOGLE EMPLOYEE ************* ****** KARTHICK KUPPURAJ M ***************** ********************************************/ #define ms(s, n) memset(s, n, sizeof(s)) #define pb push_back #define pf push_front #define mp make_pair #define f first #define s second #define prec(n) fixed<<setprecision(n) #define sll(x) scanf("%lld",&x); #define pll(x) printf("%lld",x); #define pn printf("\n"); #define ps printf(" "); #define pc(c) printf("%c",c); typedef long long int ll; #define EPS 1e-9 const int MOD = (int) 1e9 + 7; const int INF = (int) 1e9; const ll LINF = (ll) 1e18; int add(int x, int y) { x += y; if (x >= MOD) return x - MOD; return x; } int sub(int x, int y) { x -= y; if (x < 0) return x + MOD; return x; } int mult(int x, int y) { return ((ll) x * y) % MOD; } int bin_pow(int x, int p) { if (p == 0) return 1; if (p == 2 || (p & 1)) return mult(x, bin_pow(x, p - 1)); return bin_pow(bin_pow(x, p / 2), 2); } int rev(int x) { return bin_pow(x, MOD - 2); } const int N = 200100; const int K = 4010; const int Z = 2002; int n; int a[N][2]; int C[K][K]; ll b[K]; int f[2 * K], rf[2 * K]; int ans = 0; void init() { f[0] = 1; for (int i = 1; i < 2 * K; i++) f[i] = mult(f[i - 1], i); rf[2 * K - 1] = rev(f[2 * K - 1]); for (int i = 2 * K - 1; i > 0; i--) { rf[i - 1] = mult(rf[i], i); } for (int i = 0; i < K; i++) { C[i][0] = C[i][i] = 1; } for (int i = 1; i < K; i++) { for (int j = 1; j < i; j++) { C[i][j] = add(C[i - 1][j], C[i - 1][j - 1]); } } return; } void solve(int x, int y) { for (int i = -x; i <= y; i++) { b[Z - i] += C[x + y][x + i]; } return; } int getC(int n, int k) { return mult(f[n], mult(rf[k], rf[n - k])); } int main() { init(); scanf("%d", &n); for (int i = 0; i < n; i++) { for (int j = 0; j < 2; j++) { scanf("%d", &a[i][j]); } } for (int i = 0; i < n; i++) { solve(a[i][0], a[i][1]); } for (int i = -Z; i <= Z; i++) { b[Z + i] %= MOD; } for (int i = -Z; i <= Z; i++) { ans = add(ans, mult(b[Z + i], b[Z - i])); } for (int i = 0; i < n; i++) { ans = sub(ans, getC(2 * (a[i][0] + a[i][1]), 2 * a[i][0])); } if (ans & 1) ans += MOD; ans /= 2; printf("%d\n", ans); return 0; }

codenet

s159318775

p04051

cpp

Accepted

#include <algorithm> #include <bitset> #include <cmath> #include <cstdio> #include <cstring> #include <ctime> #include <deque> #include <iostream> #include <map> #include <queue> #include <set> #include <string> #include <vector> using namespace std; namespace io { #define SIZ (1 << 21 | 1) #define gc() (io::iS == io::iT ? (io::iT= (io::iS= io::ibuff) + fread(io::ibuff, 1, SIZ, stdin), (io::iS == io::iT ? EOF : *io::iS++)) : *io::iS++) #define putc(x) (io::oS == io::oT ? (fwrite(io::obuff, 1, io::oS - io::obuff, stdout), io::oS= io::obuff, (*io::oS++= x)) : *io::oS++= x) #define exit \ fwrite(io::obuff, 1, io::oS - io::obuff, stdout); \ return 0; char *iS, *iT, ibuff[SIZ], obuff[SIZ], *oS= obuff, *oT= oS + SIZ - 1, fu[110], c; int fr; template <class Type> inline void read(Type &x) { x= 0; Type y= 1; for(c= gc(); (c > '9' || c < '0') && c != '-'; c= gc()) ; c == '-' ? y= -1 : x= (c & 15); for(c= gc(); c >= '0' && c <= '9'; c= gc()) x= x * 10 + (c & 15); x*= y; } inline void reads(char *x) { for(c= gc(); c == ' ' || c == '\n'; c= gc()) ; for(; c != ' ' && c != '\n' && c != EOF; *x= c, c= gc(), ++x) ; } template <class Type> inline void print(Type x, char text= '\n') { if(x < 0) putc('-'), x*= -1; if(x == 0) putc('0'); while(x) fu[++fr]= x % 10 + '0', x/= 10; while(fr) putc(fu[fr--]); putc(text); } inline void prints(char *x, char *y= NULL, char text= '\n') { for(; *x && x != y; ++x) putc(*x); putc(text); } } // namespace io using io::print; using io::prints; using io::read; using io::reads; #define N 200001 #define M 4005 #define P 1000000007 int n, a[N], b[N], f[M][M], ans, jc[8005], invjc[8005]; inline int ksm(int a, int b) { int s= 1; for(; b; b>>= 1, a= (long long)a * a % P) if(b & 1) s= (long long)s * a % P; return s; } inline int C(int n, int m) { return (long long)jc[n] * invjc[m] % P * invjc[n - m] % P; } signed main() { read(n); for(int i= 1; i <= n; i++) read(a[i]), read(b[i]); for(int i= 1; i <= n; i++) f[2000 - a[i]][2000 - b[i]]++; for(int i= 0; i <= 4000; i++) { for(int j= 0; j <= 4000; j++) { f[i + 1][j]= ((long long)f[i + 1][j] + f[i][j]) % P; f[i][j + 1]= ((long long)f[i][j + 1] + f[i][j]) % P; } } for(int i= 1; i <= n; i++) ans= ((long long)ans + f[2000 + a[i]][2000 + b[i]]) % P; jc[0]= invjc[0]= 1; for(int i= 1; i <= 8000; i++) jc[i]= (long long)jc[i - 1] * i % P, invjc[i]= ksm(jc[i], P - 2); for(int i= 1; i <= n; i++) { ans= ((long long)ans - C(2 * (a[i] + b[i]), 2 * b[i])) % P; if(ans < 0) ans+= P; } ans= (long long)ans * ksm(2, P - 2) % P; print(ans); exit; }

codenet

s457751162

p04051

cpp

Accepted

//{ #include<bits/stdc++.h> using namespace std; typedef long long ll; typedef double lf; typedef pair<ll,ll> ii; #define REP(i,n) for(ll i=0;i<n;i++) #define REP1(i,n) for(ll i=1;i<=n;i++) #define FILL(i,n) memset(i,n,sizeof i) #define X first #define Y second #define SZ(_a) (int)_a.size() #define ALL(_a) _a.begin(),_a.end() #define pb push_back #ifdef brian #define debug(...) do{\ fprintf(stderr,"%s - %d (%s) = ",__PRETTY_FUNCTION__,__LINE__,#__VA_ARGS__);\ _do(__VA_ARGS__);\ }while(0) template<typename T>void _do(T &&_x){cerr<<_x<<endl;} template<typename T,typename ...S> void _do(T &&_x,S &&..._t){cerr<<_x<<" ,";_do(_t...);} template<typename _a,typename _b> ostream& operator << (ostream &_s,const pair<_a,_b> &_p){return _s<<"("<<_p.X<<","<<_p.Y<<")";} template<typename It> ostream& _OUTC(ostream &_s,It _ita,It _itb) { _s<<"{"; for(It _it=_ita;_it!=_itb;_it++) { _s<<(_it==_ita?"":",")<<*_it; } _s<<"}"; return _s; } template<typename _a> ostream &operator << (ostream &_s,vector<_a> &_c){return _OUTC(_s,ALL(_c));} template<typename _a> ostream &operator << (ostream &_s,set<_a> &_c){return _OUTC(_s,ALL(_c));} template<typename _a,typename _b> ostream &operator << (ostream &_s,map<_a,_b> &_c){return _OUTC(_s,ALL(_c));} template<typename _t> void pary(_t _a,_t _b){_OUTC(cerr,_a,_b);cerr<<endl;} #define IOS() #else #define debug(...) #define pary(...) #define endl '\n' #define IOS() ios_base::sync_with_stdio(0);cin.tie(0); #endif // brian //} const ll MAXn = 2e5 + 5, MAXc=5e3+5,MAXlg=__lg(MAXn)+2; const ll MOD=1000000007; const ll INF=ll(1e15); const int C = 2005; ll a[MAXn], b[MAXn], fac[4 * MAXc], dp[MAXc][MAXc]; void add(ll &x, ll y){ x += y; if (x >= MOD) x -= MOD; } ll mypw(ll x, ll k){ if (!k) return 1; ll a = mypw(x, k / 2); if (k & 1)return a * a % MOD * x % MOD; else return a * a % MOD; } ll c(ll x, ll y){ return fac[x] * mypw(fac[y], MOD - 2) % MOD * mypw(fac[x - y], MOD - 2) % MOD; } int main() { IOS(); fac[0] = 1; for(int i = 1;i < 4 * MAXc;i ++) fac[i] = fac[i - 1] * i % MOD; int n; cin >> n; for(int i = 1;i <= n;i ++) cin >> a[i] >> b[i], dp[C - a[i]][C - b[i]]++; for (int i = 1;i <= 2 * C;i ++) for(int j = 1;j <= 2 * C;j ++) add(dp[i][j], dp[i][j - 1]), add(dp[i][j], dp[i - 1][j]); ll tt = 0; for (int i = 1;i <= n;i ++) add(tt, dp[C + a[i]][C + b[i]]); debug(tt); for (int i = 1;i <= n;i ++) tt = (tt - c(a[i] + a[i] + b[i] + b[i], a[i] + a[i])) % MOD; debug((tt + MOD) % MOD); cout << (tt * mypw(2, MOD - 2) % MOD + MOD) % MOD << endl; }

codenet

s641035063

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; typedef long long ll; typedef double lf; typedef pair<int,int> ii; typedef pair<ii,int> iii; #define REP(i,n) for(int i=0;i<n;i++) #define REP1(i,n) for(int i=1;i<=n;i++) #define RST(i,n) memset(i,n,sizeof i) #define SZ(a) (int)a.size() #define ALL(a) a.begin(),a.end() #define X first #define Y second #define eb emplace_back #ifdef cold66 #define debug(...) do{\ fprintf(stderr,"LINE %d: (%s) = ",__LINE__,#__VA_ARGS__);\ _do(__VA_ARGS__);\ }while(0) template<typename T>void _do(T &&_x){cerr<<_x<<endl;} template<typename T,typename ...S> void _do(T &&_x,S &&..._t){cerr<<_x<<", ";_do(_t...);} template<typename _a,typename _b> ostream& operator << (ostream &_s,const pair<_a,_b> &_p){return _s<<"("<<_p.X<<","<<_p.Y<<")";} template<typename It> ostream& _OUTC(ostream &_s,It _ita,It _itb) { _s<<"{"; for(It _it=_ita;_it!=_itb;_it++) { _s<<(_it==_ita?"":",")<<*_it; } _s<<"}"; return _s; } template<typename _a> ostream &operator << (ostream &_s,vector<_a> &_c){return _OUTC(_s,ALL(_c));} template<typename _a> ostream &operator << (ostream &_s,set<_a> &_c){return _OUTC(_s,ALL(_c));} template<typename _a,typename _b> ostream &operator << (ostream &_s,map<_a,_b> &_c){return _OUTC(_s,ALL(_c));} template<typename _t> void pary(_t _a,_t _b){_OUTC(cerr,_a,_b);cerr<<endl;} #define IOS() #else #define debug(...) #define pary(...) #define endl '\n' #define IOS() ios_base::sync_with_stdio(0);cin.tie(0); #endif // cold66 //} template<class T> inline bool chkmax(T &a, const T &b) { return b > a ? a = b, true : false; } template<class T> inline bool chkmin(T &a, const T &b) { return b < a ? a = b, true : false; } const ll MAXn=2e5+5,MAXlg=__lg(MAXn)+2; const ll MOD=1000000007; const ll INF=0x3f3f3f3f; const ll C = 2000; const ll M = 4e3+5; int a[MAXn],b[MAXn]; int dp[M][M], grid[M][M]; int mod2 = 500000004; int add(int x,int y){ int ret = x + y; if (ret >= MOD) ret -= MOD; return ret; } int sub(int x,int y){ int ret = x - y; if (ret < 0) ret += MOD; return ret; } int main(){ IOS(); int n; cin >> n; REP (i,n) { cin >> a[i] >> b[i]; dp[a[i]+C][b[i]+C]++; } for (int i=2*C;i>=0;i--) { for (int j=2*C;j>=0;j--) { dp[i][j] = add(dp[i][j],add(dp[i+1][j],dp[i][j+1])); } } grid[0][0] = 1; REP (i,2*C+1) REP (j,2*C+1) { if (i) grid[i][j] = add(grid[i][j],grid[i-1][j]); if (j) grid[i][j] = add(grid[i][j],grid[i][j-1]); } ll ans = 0; REP (i,n) { ans = add(ans,dp[C-a[i]][C-b[i]]); ans = sub(ans,grid[2*a[i]][2*b[i]]); } ans = ans*mod2 % MOD; cout << ans << endl; }

codenet

s689504742

p04051

cpp

Accepted

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; //template #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(a);i>(b);i--) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12; string to_str(ll x){string res; while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return res;} template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; } template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; } //template end template<unsigned mod>struct mint { int val; int inv() const{ int tmp,a=val,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0)x+=mod; return x; } mint():val(0){} mint(ll x):val(x>=0?x%mod:mod+(x%mod)){} mint pow(ll t){mint res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;} mint& operator+=(const mint& x){if((val+=x.val)>=mod)val-=mod;return *this;} mint& operator-=(const mint& x){if((val+=mod-x.val)>=mod)val-=mod; return *this;} mint& operator*=(const mint& x){val=(ll)val*x.val%mod; return *this;} mint& operator/=(const mint& x){val=(ll)val*x.inv()%mod; return *this;} mint operator+(const mint& x)const{return mint(*this)+=x;} mint operator-(const mint& x)const{return mint(*this)-=x;} mint operator*(const mint& x)const{return mint(*this)*=x;} mint operator/(const mint& x)const{return mint(*this)/=x;} bool operator==(const mint& x)const{return val==x.val;} bool operator!=(const mint& x)const{return val!=x.val;} }; using Mint=mint<1000000007>; struct factorial { vector<Mint> Fact, Finv; public: factorial(int maxx){ Fact.resize(maxx+1),Finv.resize(maxx+1); Fact[0]=Mint(1); rep(i,0,maxx)Fact[i+1]=Fact[i]*(i+1); Finv[maxx]=Mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*i; } Mint fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} Mint nPr(int n,int r){if(n<0||n<r||r<0)return Mint(0);else return Fact[n]*Finv[n-r];} Mint nCr(int n,int r){if(n<0||n<r||r<0)return Mint(0);else return Fact[n]*Finv[r]*Finv[n-r];} }; Mint dp[4050][4050]; int main(){ int n; scanf("%d",&n); map<pair<int,int>,int> mp; rep(i,0,n){ int x,y; scanf("%d%d",&x,&y); mp[{x,y}]++; } for(auto p:mp)dp[2010-p.first.first][2010-p.first.second]+=p.second; rep(i,1,4030)rep(j,1,4030)dp[i][j]+=dp[i-1][j]+dp[i][j-1]; Mint res; factorial fact(8020); for(auto p:mp){ res+=dp[2010+p.first.first][2010+p.first.second]*p.second; res-=fact.nCr((p.first.first+p.first.second)*2,p.first.first*2)*p.second; } res/=2; printf("%d\n",res.val); return 0; }

codenet

s757283760

p04051

cpp

Accepted

#include<bits/stdc++.h> using namespace std; using Int = long long; #define MOD 1000000007 #define MAX_P 200005 Int fact[MAX_P],inv[MAX_P],finv[MAX_P];; Int extgcd(Int a,Int b,Int& x,Int& y){ Int d=a; if(b!=0){ d=extgcd(b,a%b,y,x); y-=(a/b)*x; }else{ x=1;y=0; } return d; } Int mod_inverse(Int a,Int mod){ Int x,y; extgcd(a,mod,x,y); return (mod+x%mod)%mod; } Int mod_pow(Int x,Int n,Int mod){ Int res=1; while(n){ if(n&1) (res*=x)%=mod; (x*=x)%=mod; n>>=1; } return res; } Int mod_inverse2(Int a,Int mod){ return mod_pow(a,mod-2,mod); } void init(Int mod){ fact[0]=1; for(Int i=1;i<MAX_P;i++) fact[i]=(fact[i-1]*i)%mod; inv[1]=1; for(Int i=2;i<MAX_P;i++) inv[i]=inv[mod%i]*(mod-mod/i)%mod; finv[0]=1; for(Int i=1;i<MAX_P;i++) finv[i]=finv[i-1]*inv[i]%mod; } Int mod_fact(Int n,Int mod,Int& e){ e=0; if(n==0) return 1; Int res=mod_fact(n/mod,mod,e); e+=n/mod; if(n/mod%2!=0)return res*(mod-fact[n%mod]) %mod; return res*fact[n%mod]%mod; } Int mod_comb(Int n,Int k,Int mod){ if(n==k||k==0) return 1; Int e1,e2,e3; Int a1=mod_fact(n,mod,e1),a2=mod_fact(k,mod,e2),a3=mod_fact(n-k,mod,e3); if(e1>e2+e3) return 0; return a1*mod_inverse(a2*a3%mod,mod)%mod; } Int mod_comb2(Int n,Int k,Int mod){ Int res=1; for(Int i=0;i<k;i++){ res*=(n-i)%mod; res%=mod; res*=mod_inverse(i+1,mod); res%=mod; } return res; } //only for prime mod Int mod_comb3(Int n,Int k,Int mod){ if(k<0||k>n) return 0; return fact[n]*finv[k]%mod*finv[n-k]%mod; } Int montmort(Int n,Int mod){ Int res=0,inv=1; for(Int k=2;k<=n;k++){ (inv*=mod_inverse(k,mod))%=mod; if(k%2) (res+=mod-inv)%=mod; else (res+=inv)%=mod; } for(Int i=1;i<=n;i++) (res*=i)%=mod; return res; } // calculate P(t) from given points in [0,N] Int LagrangePolynomial(vector<Int> &y,Int t,const Int mod){ init(mod); Int n=y.size()-1; Int num=1; for(Int i=0;i<=n;i++) num=num*((t-i)%mod)%mod; Int res=0; for(Int i=0;i<=n;i++){ Int tmp=(y[i]*num%mod)*mod_inverse((t-i)%mod,mod)%mod; tmp=tmp*finv[i]%mod; tmp=tmp*finv[n-i]%mod; if((n-i)&1) tmp=mod-tmp; res=(res+tmp)%mod; } return res; } //INSERT ABOVE HERE Int dp[5050][5050]; signed main(){ memset(dp,0,sizeof(dp)); Int n; cin>>n; vector<Int> a(n),b(n); for(Int i=0;i<n;i++){ cin>>a[i]>>b[i]; dp[2500-a[i]][2500-b[i]]++; } for(Int i=1;i<5000;i++) for(Int j=1;j<5000;j++) dp[i][j]=(dp[i][j]+dp[i-1][j]+dp[i][j-1])%MOD; Int ans=0; for(Int i=0;i<n;i++) ans=(ans+dp[2500+a[i]][2500+b[i]])%MOD; init(MOD); for(Int i=0;i<n;i++) ans=(ans+MOD-mod_comb3((a[i]+b[i])*2,a[i]*2,MOD))%MOD; ans=ans*mod_inverse(2,MOD)%MOD; cout<<ans<<endl; return 0; }

codenet

s733935923

p04051

cpp

Accepted

// Words are flowing out like endless rain into a paper cup // They slither while they pass they slip away across the universe // Pools of sorrow, waves of joy are drifting through my open mind // Possessing and caressing me #include <bits/stdc++.h> using namespace std; using LL = long long; namespace _buff { const size_t BUFF = 1 << 19; char ibuf[BUFF], *ib = ibuf, *ie = ibuf; char getc() { if (ib == ie) { ib = ibuf; ie = ibuf + fread(ibuf, 1, BUFF, stdin); } return ib == ie ? -1 : *ib++; } } LL read() { using namespace _buff; LL ret = 0; bool pos = true; char c = getc(); for (; (c < '0' || c > '9') && c != '-'; c = getc()) { assert(~c); } if (c == '-') { pos = false; c = getc(); } for (; c >= '0' && c <= '9'; c = getc()) { ret = (ret << 3) + (ret << 1) + (c ^ 48); } return pos ? ret : -ret; } using uint = unsigned; const uint MOD = 1E9 + 7; struct Z { uint v; Z(uint v = 0) : v(v) {} Z& operator += (const Z &z) { v += z.v; if (v >= MOD) v -= MOD; return *this; } Z& operator -= (const Z &z) { if (v < z.v) v += MOD; v -= z.v; return *this; } Z& operator *= (const Z &z) { v = static_cast<uint64_t>(v) * z.v % MOD; return *this; } }; ostream& operator << (ostream &os, const Z &z) { return os << z.v; } Z operator + (const Z &x, const Z &y) { return Z(x.v + y.v >= MOD ? x.v + y.v - MOD : x.v + y.v); } Z operator - (const Z &x, const Z &y) { return Z(x.v < y.v ? x.v + MOD - y.v : x.v - y.v); } Z operator * (const Z &x, const Z &y) { return Z(static_cast<uint64_t>(x.v) * y.v % MOD); } Z qpow(Z base, uint e) { Z ret(1); for (; e; e >>= 1) { if (e & 1) { ret *= base; } base *= base; } return ret; } const size_t N = 2E5 + 5; const size_t S = 2E3 + 2; const size_t M = 4E3 + 5; const size_t L = 8E3 + 5; int n, a[N], b[N]; Z fac[L], inv[L], f[M][M]; void prep() { fac[0] = 1; for (uint i = 1; i < L; ++i) { fac[i] = fac[i - 1] * i; } inv[L - 1] = qpow(fac[L - 1], MOD - 2); for (uint i = L; --i; ) { inv[i - 1] = inv[i] * i; } } int main() { prep(); n = read(); for (int i = 0; i < n; ++i) { a[i] = read(); b[i] = read(); f[S - a[i]][S - b[i]] += 1; } for (uint i = 1; i < M; ++i) { for (uint j = 1; j < M; ++j) { f[i][j] += f[i - 1][j] + f[i][j - 1]; } } Z ans = 0; for (int i = 0; i < n; ++i) { ans += f[S + a[i]][S + b[i]]; ans -= fac[(a[i] + b[i]) << 1] * inv[a[i] << 1] * inv[b[i] << 1]; } ans *= (MOD + 1) >> 1; cout << ans; return 0; }

codenet

s104856820

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define Gene template< class #define Rics printer& operator, Gene c> struct rge{c b, e;}; Gene c> rge<c> range(c i, c j){ return {i, j};} struct printer{ ~printer(){cerr<<endl;} Gene c >Rics(c x){ cerr<<boolalpha<<x; return *this;} Rics(string x){cerr<<x;return *this;} Gene c, class d >Rics(pair<c, d> x){ return *this,"(",x.first,", ",x.second,")";} Gene ... d, Gene ...> class c >Rics(c<d...> x){ return *this, range(begin(x), end(x));} Gene c >Rics(rge<c> x){ *this,"["; for(auto it = x.b; it != x.e; ++it) *this,(it==x.b?"":", "),*it; return *this,"]";} }; #define debug() cerr<<"LINE "<<__LINE__<<" >> ", printer() #define dbg(x) "[",#x,": ",(x),"] " mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); int my_rand(int l, int r) { return uniform_int_distribution<int>(l, r) (rng); } const int N = 100000; const int mod = 1e9 + 7; namespace NT { int fact[N], inv[N]; int bm(int b, int p, int m) { if(p == 0) return 1%m; int t = bm(b,p/2,m); t = (1ll*t*t)%m; if(p&1) return 1ll*t*b%m; return t; } int C(int n, int r) { if(n < 0 or r < 0 or r > n) return 0; int ret = 1ll*fact[n]*inv[r]%mod; ret = 1ll*ret*inv[n-r]%mod; return ret; } void init() { fact[0] = 1; for(int i = 1; i < N; i++) { fact[i] = 1ll*fact[i-1]*i%mod; } inv[N-1] = bm(fact[N-1], mod-2, mod); for(int i = N-2; i >= 0; i--) { inv[i] = 1ll*inv[i+1]*(i+1)%mod; } } bool composite[N]; vector<int> prime; void sieve() { composite[1] = 1; for(int i = 2; i < N; i++) { if(!composite[i]) prime.push_back(i); for(int j = 0; j < prime.size() && prime[j]*i < N; j++) { composite[prime[j] * i] = 1; if(i%prime[j] == 0) break; } } } } const int M = 4005, B = 2001; int dp[M][M]; int main() { // freopen("in.txt", "r", stdin); ios::sync_with_stdio(0); cin.tie(0); NT::init(); int n; cin >> n; int sub = 0, ans = 0; vector<int> a(n), b(n); for(int i = 0; i < n; i++) { int x, y; cin >> x >> y; sub += NT::C(2*(x+y), 2*x); sub %= mod; dp[-x+B][-y+B]++; a[i] = x+B, b[i] = y+B; } for(int i = 1; i < M; i++) { for(int j = 1; j < M; j++) { dp[i][j] += dp[i-1][j] + dp[i][j-1]; dp[i][j] %= mod; } } for(int i = 0; i < n; i++) { ans += dp[a[i]][b[i]]; ans %= mod; } ans -= sub; ans %= mod; ans = 1ll*ans*((mod+1)/2)%mod; if(ans < 0) ans += mod; cout << ans << endl; }

codenet

s724801727

p04051

cpp

Accepted

#include <bits/stdc++.h> #define rf(x) (x)=0;while(*p<48)p++;while(47<*p)(x)=((x)<<3)+((x)<<1)+(*p++&15); //#define rf(x) (x)=0;while(*p<48)im=*p=='-';while(47<*p)(x)=((x)<<3)+((x)<<1)+(*p++&15);if(im)(x)=-(x); #define pb push_back #define sz(V) ((int)(V).size()) #define allv(V) ((V).begin()),((V).end()) #define befv(V) ((V)[(sz(V)-2)]) #define sorv(V) sort(allv(V)) #define revv(V) reverse(allv(V)) #define univ(V) (V).erase(unique(allv(V)),(V).end()) #define clv(V) (V).clear() #define upmin(a,b) (a)=min((a),(b)) #define upmax(a,b) (a)=max((a),(b)) #define rb(x) ((x)&(-(x))) #define cb(x) (x)=(!(x)) #define INF (0x3f3f3f3f) #define INFLL (0x3f3f3f3f3f3f3f3fll) #define INFST (0x7f7f7f7f) #define INFLLST (0x7f7f7f7f7f7f7f7fll) using namespace std; typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef pair<int, ll> pil; typedef pair<ll, int> pli; typedef pair<ld, ld> pdd; typedef complex<ld> base; const ld EPS = (ld)1e-7; const ld PI = acos(0) * 2; bool isZero(const ld& x) { return abs(x) <= EPS; } int sign(const ld& x) { return isZero(x) ? 0 : (0 < x ? 1 : -1); } ll gcd(ll a, ll b) { for(;b;a%=b,swap(a,b)){} return abs(a); } pll operator + (const pll& a, const pll& b) { return pll(a.first+b.first, a.second+b.second); } pll operator - (const pll& a, const pll& b) { return pll(a.first-b.first, a.second-b.second); } pll operator * (const pll& a, const ll& b) { return pll(a.first*b, a.second*b); } ll operator * (const pll& a, const pll& b) { return a.first*b.second - b.first*a.second; } ll ccw(const pll& a, const pll& b, const pll& c) { return a*b + b*c + c*a; } void fg(vector<int> G[], int a, int b) { G[a].pb(b); G[b].pb(a); } void fg(vector<pii> G[], int a, int b, int c) { G[a].pb({b, c}); G[b].pb({a, c}); } const int MOD = 1000000007; const int MAXN = 200005; const int MAXX = 2005; int d[MAXX*2][MAXX*2]; ll fac[MAXX*8], invfac[MAXX*8]; int A[MAXN], B[MAXN]; int N, Ans; ll pw(ll n, ll k) { ll r = 1; for(n %= MOD; k; k >>= 1) { if(k&1) r = r * n % MOD; n = n * n % MOD; } return r; } int main() { ios::sync_with_stdio(false); fac[0] = 1; for(int i = 1; i < MAXX*8; i++) fac[i] = fac[i-1] * i % MOD; invfac[MAXX*8-1] = pw(fac[MAXX*8-1], MOD-2); for(int i = MAXX*8-1; i; i--) invfac[i-1] = invfac[i] * i % MOD; cin >> N; for(int i = 0; i < N; i++) { cin >> A[i] >> B[i]; d[-A[i]+MAXX][-B[i]+MAXX]++; } for(int i = 1; i < MAXX*2; i++) for(int j = 1; j < MAXX*2; j++) d[i][j] = (d[i][j] + (d[i-1][j] + d[i][j-1]) % MOD) % MOD; for(int i = 0; i < N; i++) { Ans = (Ans + d[A[i]+MAXX][B[i]+MAXX]) % MOD; Ans = (Ans - fac[A[i]*2+B[i]*2] * invfac[A[i]*2] % MOD * invfac[B[i]*2] % MOD + MOD) % MOD; } Ans = (ll)Ans * pw(2, MOD-2) % MOD; cout << Ans << endl; return 0; }

codenet

s763260218

p04051

cpp

Accepted

#define _CRT_SECURE_NO_WARNINGS #include <cstdio> #include <vector> #include <string> #include <iostream> #include <algorithm> #include <map> #include <iterator> #include <functional> #include <set> #include <stack> #include <queue> #include <deque> #include <fstream> #include <iomanip> #include <unordered_map> #include <unordered_set> #include <numeric> #include <cmath> #include <list> #include <sstream> #include <tuple> #include <complex> #include <stdio.h> using namespace std; #pragma GCC optimize("O3") #pragma GCC target("sse4") typedef double LD; typedef long long LL; typedef pair<int, int> PII; typedef pair<LD, LD> PDD; typedef pair<LL, LL> PLL; typedef vector<int> VI; typedef vector<LL> VLL; typedef vector<char> VCH; typedef vector<LD> VLD; typedef vector<VI> VVI; typedef vector<VLL> VVLL; typedef vector<VCH> VVCH; typedef vector<PII> VPII; typedef vector<PLL> VPLL; typedef vector<PDD> VPDD; #define MP make_pair #define PB push_back #define X first #define Y second #define next fake_next #define previous fake_previous #define left fake_left #define right fake_right #define FOR(i,a,b) for(int i = (a); i < (b); ++i) #define RFOR(i,b,a) for(int i = (b) - 1; i >= (a); --i) #define REP(i, t) FOR(i,0,t) #define ALL(a) a.begin(), a.end() #define SZ(a) (int)((a).size()) const LD PI = acos(-1.0); const LL mod = 1000000007; const LL INF = 1e9; const LL MAXN = 4001; const LL MAXK = 2000; int n; VLL a; VLL b; VLL fact; VLL revFact; VVLL DP1; VVLL DP2; inline LL power(LL x, LL to) { LL res = 1; while (to) { if (to & 1) res = (res * x) % mod; x = (x*x) % mod; to >>= 1; } return res; } LL solve() { //C(2a, 2b); LL res = 0, add; FOR(i, 0, n) { add = (fact[a[i] * 2 + b[i] * 2]) * revFact[a[i] * 2] % mod; add *= revFact[b[i] * 2]; add %= mod; res += add; } res %= mod; return res; } LL calculate() { DP1.assign(MAXN, VLL(MAXN, 0)); DP2.assign(MAXN, VLL(MAXN, 0)); FOR(i, 0, n) DP2[a[i] + MAXK][b[i] + MAXK]++, DP1[MAXK - a[i]][MAXK - b[i]]++; FOR(i, 0, MAXN) FOR(j, 0, MAXN) { if (i) DP1[i][j] = (DP1[i][j] + DP1[i - 1][j]) % mod; if (j) DP1[i][j] = (DP1[i][j] + DP1[i][j - 1]) % mod; } LL ans = 0; FOR(i, 0, MAXN) FOR(j, 0, MAXN) { ans += (DP1[i][j] * DP2[i][j]) % mod; ans %= mod; } ans %= mod; return ans; } int main() { ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); //freopen("In.txt", "r", stdin); fact.assign(MAXN*2, 0); revFact.assign(MAXN * 2, 0); fact[0] = 1; FOR(i, 1, MAXN*2) fact[i] = (fact[i - 1] * i) % mod; FOR(i, 1, MAXN*2) revFact[i] = power(fact[i], mod - 2); cin >> n; a.assign(n, 0); b.assign(n, 0); FOR(i, 0, n) cin >> a[i] >> b[i]; LL ans = calculate(); ans += mod; ans -= solve(); ans %= mod; ans *= power(2, mod - 2); ans %= mod; cout << ans << endl; cin >> n; return 0; }

codenet

s699597540

p04051

cpp

Accepted

#include <map> #include <set> #include <queue> #include <vector> #include <cstdio> #include <cstring> #include <iostream> #include <algorithm> namespace remoon { #define re register #define de double #define le long double #define ri register int #define ll long long #define sh short #define ui unsiged int #define ull unsigned long long #define pii pair<int, int> #define mp make_pair #define pb push_back #define fi first #define se second #define tpr template <typename ra> #define rep(iu, st, ed) for(ri iu = st; iu <= ed; iu ++) #define drep(iu, ed, st) for(ri iu = ed; iu >= st; iu --) #define gc getchar inline int read() { int p = 0, w = 1; char c = gc(); while(c > '9' || c < '0') { if(c == '-') w = -1; c = gc(); } while(c >= '0' && c <= '9') p = p * 10 + c - '0', c = gc(); return p * w; } int wr[50], rw; #define pc(iw) putchar(iw) tpr inline void write(ra o, char c = '\n') { if(!o) pc('0'); if(o < 0) o = -o, pc('-'); while(o) wr[++ rw] = o % 10, o /= 10; while(rw) pc(wr[rw --] + '0'); pc(c); } tpr inline void cmin(ra &a, ra b) { if(a > b) a = b; } tpr inline void cmax(ra &a, ra b) { if(a < b) a = b; } tpr inline bool ckmin(ra &a, ra b) { return (a > b) ? a = b, 1 : 0; } tpr inline bool ckmax(ra &a, ra b) { return (a < b) ? a = b, 1 : 0; } } using namespace std; using namespace remoon; namespace mod_zone { #define mod 1000000007 inline void inc(int &a, int b) { a += b; if(a >= mod) a -= mod; } inline void dec(int &a, int b) { a -= b; if(a < 0) a += mod; } inline int Inc(int a, int b) { return (a + b >= mod) ? a + b - mod : a + b; } inline int Dec(int a, int b) { return (a - b < 0) ? a - b + mod : a - b; } inline int mul(int a, int b) { return 1ll * a * b % mod; } inline int fp(int a, int k) { int ret = 1; for( ; k; k >>= 1, a = mul(a, a)) if(k & 1) ret = mul(ret, a); return ret; } } using namespace mod_zone; #define sid 4055 int n; int a[200050], b[200050]; int f[sid][sid], jc[sid * 2], ny[sid * 2]; inline void Init() { jc[0] = jc[1] = 1; ny[0] = ny[1] = 1; rep(i, 2, 8000) { jc[i] = mul(jc[i - 1], i); ny[i] = mul(mod - mod / i, ny[mod % i]); } rep(i, 2, 8000) ny[i] = mul(ny[i], ny[i - 1]); } inline int calc() { int ret = 0; rep(i, 1, n) f[2005 - a[i]][2005 - b[i]] ++; rep(i, 1, 4010) rep(j, 1, 4010) inc(f[i][j], Inc(f[i][j - 1], f[i - 1][j])); rep(i, 1, n) inc(ret, f[2005 + a[i]][2005 + b[i]]); return ret; } inline int C(int n, int m) { return mul(mul(jc[n], ny[m]), ny[n - m]); } inline int solve() { int ret = 0; rep(i, 1, n) inc(ret, C((a[i] + b[i]) << 1, a[i] << 1)); return ret; } int main() { Init(); n = read(); rep(i, 1, n) a[i] = read(), b[i] = read(); write(mul(Dec(calc(), solve()), fp(2, mod - 2))); return 0; }

codenet

s857483950

p04051

cpp

Accepted

#include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> #define IN freopen("perimetric_chapter_1_input.txt","r",stdin) #define OUT freopen("output.txt","w",stdout) #define pb push_back #define mp make_pair #define FOR(i,a,b) for(i=a ; i<=b ; i++) #define DBG printf("Hi\n") #define i64 long long int #define ui64 unsigned long long int #define xx first #define yy second #define ln 17 #define off 2002 #define sq(x) ((x)*(x)) #define FASTIO ios_base::sync_with_stdio(false); cin.tie(NULL) using namespace __gnu_pbds; using namespace std ; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); typedef tree< i64, null_type, less<i64>, rb_tree_tag, tree_order_statistics_node_update> ordered_set; typedef pair<int,int> pii; #define log 20 #define mod 1000000007LL #define INF 1000000000000000000LL #define maxn 300005 const long double eps = 1e-9 ; class numberTheory{ public: numberTheory(){} pii extendedEuclid(i64 a, i64 b) { // returns x, y | ax + by = gcd(a,b) if(b == 0) return pii( a >= 0 ? 1 : -1 , 0LL); else { pii d = extendedEuclid(b, a % b); return pii(d.yy, d.xx - d.yy * (a / b)); } } i64 modularInverse(i64 a, i64 n) { pair<i64,i64> ret = extendedEuclid(a, n); return ((ret.xx % n) + n) % n; } i64 bigMod(i64 a, i64 n , i64 m) { if(n==0) return 1 ; i64 ret = bigMod(a,n/2,m) ; ret = (ret*ret)%m ; if(n%2) ret = (ret*a)%m ; return ret ; } }; const i64 N = 700000 ; i64 fact[N+5] , invFact[N+5] ; i64 C(i64 n, i64 r) { if( n<0 || r<0 || r>n ) return 0 ; // if(n<=50) return cc[n][r] ; i64 ret = (fact[n]*invFact[r])%mod ; return (ret*invFact[n-r])%mod ; } void preprocess() { numberTheory nt ; fact[0] = 1 ; for(i64 x=1 ; x<=N ; x++) fact[x] = (fact[x-1]*x)%mod ; invFact[N] = nt.modularInverse(fact[N],mod) ; for(i64 x=N-1 ; x>=0 ; x--) invFact[x] = (invFact[x+1]*(x+1) )%mod ; } pair<int,int> ara[maxn] ; int dp[4015][4015] ; int main() { preprocess() ; int n ; scanf("%d",&n) ; for(int i=1 ; i<=n ; i++) scanf("%d %d",&ara[i].xx,&ara[i].yy) ; for(int i=1 ; i<=n ; i++) { dp[ -ara[i].xx + off ][ -ara[i].yy+off ]++ ; } for(int i=-2000 ; i<=2000; i++) { for(int j=-2000 ; j<=2000 ; j++) { dp[ i+off ][ j+off ] = ( dp[i+off][j+off] + dp[i-1+off][j+off] + dp[i+off][j-1+off] )%mod ; } } int ans = 0 ; for(int i=1 ; i<=n ; i++) { ans = ( ans + dp[ ara[i].xx+off ][ ara[i].yy+off ] )%mod ; ans = ( ans - C( 2*(ara[i].xx+ara[i].yy) , 2*ara[i].xx ) )%mod ; ans = ( ans%mod + mod )%mod ; } if(ans%2) ans += mod ; ans /= 2 ; ans = (ans%mod + mod)%mod ; printf("%d\n",ans) ; return 0 ; }

codenet

s555825328

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; typedef long long int ll; typedef unsigned int uint; typedef unsigned char uchar; typedef unsigned long long ull; typedef pair<int, int> pii; typedef pair<ll, ll> pll; typedef vector<int> vi; #define REP(i,x) for(int i=0;i<(int)(x);i++) #define REPS(i,x) for(int i=1;i<=(int)(x);i++) #define RREP(i,x) for(int i=((int)(x)-1);i>=0;i--) #define RREPS(i,x) for(int i=((int)(x));i>0;i--) #define FOR(i,c) for(__typeof((c).begin())i=(c).begin();i!=(c).end();i++) #define RFOR(i,c) for(__typeof((c).rbegin())i=(c).rbegin();i!=(c).rend();i++) #define ALL(container) (container).begin(), (container).end() #define RALL(container) (container).rbegin(), (container).rend() #define SZ(container) ((int)container.size()) #define mp(a,b) make_pair(a, b) #define pb push_back #define eb emplace_back #define UNIQUE(v) v.erase( unique(v.begin(), v.end()), v.end() ); template<class T> bool chmax(T &a, const T &b) { if (a<b) { a=b; return 1; } return 0; } template<class T> bool chmin(T &a, const T &b) { if (a>b) { a=b; return 1; } return 0; } template<class T> ostream& operator<<(ostream &os, const vector<T> &t) { os<<"["; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"]"; return os; } template<class T> ostream& operator<<(ostream &os, const set<T> &t) { os<<"{"; FOR(it,t) {if(it!=t.begin()) os<<","; os<<*it;} os<<"}"; return os; } template<class S, class T> ostream& operator<<(ostream &os, const pair<S,T> &t) { return os<<"("<<t.first<<","<<t.second<<")";} template<class S, class T> pair<S,T> operator+(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first+t.first, s.second+t.second);} template<class S, class T> pair<S,T> operator-(const pair<S,T> &s, const pair<S,T> &t){ return pair<S,T>(s.first-t.first, s.second-t.second);} const int INF = 1<<28; const double EPS = 1e-8; const int MOD = 1000000007; template<int N, int MOD> struct Comb { ll fact[N + 1], inv[N + 1]; Comb() { fact[0] = inv[0] = inv[1] = 1; for (int i = 2; i <= N; i++) inv[i] = (MOD + ((ll)-inv[MOD%i] * (MOD / i)) % MOD) % MOD; REPS(i, N) { fact[i] = fact[i - 1] * i%MOD; inv[i] = inv[i] * inv[i - 1] % MOD; } } ll operator()(int n, int r) { if (n < 0 || r < 0 || r > n) return 0; ll res = inv[r] * inv[n - r]; if (res >= MOD) res %= MOD; res *= fact[n]; if (res >= MOD) res %= MOD; return res; } }; Comb<300000, MOD> C; const int INV2 = (MOD + 1) / 2; int T, n, m; int d[4002][4002], out[4002][4002]; int main(int argc, char *argv[]){ ios::sync_with_stdio(false); cin >> n; ll ans = 0; REP(i, n) { int a, b; cin >> a >> b; d[2000 - a][2000 - b] ++; out[2000 + a][2000 + b] ++; ans = ans + MOD - C(2*a + 2*b, 2*a); } REP(i, 4001)REP(j, 4001) { if (out[i][j]) { ans += (ll)d[i][j] * out[i][j] % MOD; } d[i + 1][j] = (d[i + 1][j] + d[i][j]) % MOD; d[i][j + 1] = (d[i][j + 1] + d[i][j]) % MOD; } cout << ans % MOD * INV2 % MOD << endl; return 0; }

codenet

s357522676

p04051

cpp

Accepted

#include <bits/stdc++.h> #define rep(a,n) for (ll a = 0; a < (n); ++a) #define _GLIBCXX_DEBUG using namespace std; typedef long long ll; typedef pair<ll,ll> P; typedef vector<vector<ll> > Graph; template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } const ll INF = 1e18; // auto mod int // https://youtu.be/L8grWxBlIZ4?t=9858 // https://youtu.be/ERZuLAxZffQ?t=4807 : optimize // https://youtu.be/8uowVvQ_-Mo?t=1329 : division const int mod = 1000000007; //const int mod = 998244353; struct mint { ll x; // typedef long long ll; mint(ll x=0):x((x%mod+mod)%mod){} mint operator-() const { return mint(-x);} mint& operator+=(const mint a) { if ((x += a.x) >= mod) x -= mod; return *this; } mint& operator-=(const mint a) { if ((x += mod-a.x) >= mod) x -= mod; return *this; } mint& operator*=(const mint a) { (x *= a.x) %= mod; return *this;} mint operator+(const mint a) const { return mint(*this) += a;} mint operator-(const mint a) const { return mint(*this) -= a;} mint operator*(const mint a) const { return mint(*this) *= a;} mint pow(ll t) const { if (!t) return 1; mint a = pow(t>>1); a *= a; if (t&1) a *= *this; return a; } // for prime mod mint inv() const { return pow(mod-2);} mint& operator/=(const mint a) { return *this *= a.inv();} mint operator/(const mint a) const { return mint(*this) /= a;} }; istream& operator>>(istream& is, const mint& a) { return is >> a.x;} ostream& operator<<(ostream& os, const mint& a) { return os << a.x;} // combination mod prime // mintが必要 // https://www.youtube.com/watch?v=8uowVvQ_-Mo&feature=youtu.be&t=1619 struct combination { vector<mint> fact, ifact; combination(int n):fact(n+1),ifact(n+1) { assert(n < mod); fact[0] = 1; for (int i = 1; i <= n; ++i) fact[i] = fact[i-1]*i; ifact[n] = fact[n].inv(); for (int i = n; i >= 1; --i) ifact[i-1] = ifact[i]*i; } mint operator()(int n, int k) { if (k < 0 || k > n) return 0; return fact[n]*ifact[k]*ifact[n-k]; } }; int const MAX = 2500; mint dp[2*MAX][2*MAX]; int main(){ ll n; cin >> n; vector<P>s(n); rep(i,n){ int a,b; cin >> a >> b; s[i]={a,b}; } map<P,int>mp; combination comb(1e5); rep(i,n){ mp[s[i]]++; } mint ans = 0; for(auto it=mp.begin();it!=mp.end();it++){ dp[MAX-it->first.first][MAX-it->first.second]+=it->second; } rep(i,2*MAX-1){ rep(j,2*MAX-1){ dp[i+1][j+1]+=dp[i][j+1]+dp[i+1][j]; } } for(auto it=mp.begin();it!=mp.end();it++){ ans += dp[it->first.first+MAX][it->first.second+MAX]*it->second; } rep(i,n){ P p = s[i]; int a = p.first; int b = p.second; ans -= comb(2*a+b*2,2*a); } ans /= 2; cout << ans << endl; return 0; }

codenet

s313774699

p04051

cpp

Accepted

/* created by scarlyw */ #include <cstdio> #include <string> #include <algorithm> #include <cstring> #include <iostream> #include <cmath> #include <cctype> #include <vector> #include <set> #include <queue> #include <ctime> #include <deque> #include <iomanip> #include <iterator> #include <map> inline char read() { static const int IN_LEN = 1024 * 1024; static char buf[IN_LEN], *s, *t; if (s == t) { t = (s = buf) + fread(buf, 1, IN_LEN, stdin); if (s == t) return -1; } return *s++; } // /* template<class T> inline void R(T &x) { static char c; static bool iosig; for (c = read(), iosig = false; !isdigit(c); c = read()) { if (c == -1) return ; if (c == '-') iosig = true; } for (x = 0; isdigit(c); c = read()) x = ((x << 2) + x << 1) + (c ^ '0'); if (iosig) x = -x; } //*/ const int OUT_LEN = 1024 * 1024; char obuf[OUT_LEN], *oh = obuf; inline void write_char(char c) { if (oh == obuf + OUT_LEN) fwrite(obuf, 1, OUT_LEN, stdout), oh = obuf; *oh++ = c; } template<class T> inline void W(T x) { static int buf[30], cnt; if (x == 0) write_char('0'); else { if (x < 0) write_char('-'), x = -x; for (cnt = 0; x; x /= 10) buf[++cnt] = x % 10 + 48; while (cnt) write_char(buf[cnt--]); } } inline void flush() { fwrite(obuf, 1, oh - obuf, stdout); } /* template<class T> inline void R(T &x) { static char c; static bool iosig; for (c = getchar(), iosig = false; !isdigit(c); c = getchar()) { if (c == -1) return ; if (c == '-') iosig = true; } for (x = 0; isdigit(c); c = getchar()) x = ((x << 2) + x << 1) + (c ^ '0'); if (iosig) x = -x; } // */ const int MAXM = 8000 + 33; const int MAXN = 4000 + 33; const int MAXX = 2000 + 5; const int mod = 1000000000 + 7; const int MAXC = 200000 + 11; int n; int start[MAXN][MAXN], fac[MAXM], inv_fac[MAXM], a[MAXC], b[MAXC]; int dp[MAXN][MAXN]; inline int mod_pow(int a, int b) { int ans = 1; for (; b; b >>= 1, a = (long long)a * a % mod) if (b & 1) ans = (long long)ans * a % mod; return ans; } inline int c(int n, int m) { return (n < m) ? (0) : ((long long)fac[n] * inv_fac[m] % mod * inv_fac[n - m] % mod); } inline void add(int &x, int t) { x += t, (x >= mod) ? (x -= mod) : x; } inline void solve() { R(n), fac[0] = 1; for (int i = 1; i <= n; ++i) R(a[i]), R(b[i]), start[MAXX - a[i]][MAXX - b[i]]++; for (int i = 1; i < MAXM; ++i) fac[i] = (long long)fac[i - 1] * i % mod; inv_fac[MAXM - 1] = mod_pow(fac[MAXM - 1], mod - 2); for (int i = MAXM - 2; i >= 0; --i) inv_fac[i] = (long long)inv_fac[i + 1] * (i + 1) % mod; for (int i = 1; i < MAXN; ++i) for (int j = 1; j < MAXN; ++j) dp[i][j] = (dp[i - 1][j] + dp[i][j - 1] + start[i][j]) % mod; int ans = 0; for (int i = 1; i <= n; ++i) add(ans, dp[MAXX + a[i]][MAXX + b[i]]); for (int i = 1; i <= n; ++i) add(ans, mod - c(a[i] + a[i] + b[i] + b[i], a[i] + a[i])); std::cout << ((long long)ans * (mod + 1) / 2) % mod; } int main() { // freopen("in.in", "r", stdin); solve(); return 0; }

codenet

s846295371

p04051

cpp

Accepted

#define DEB #include<bits/stdc++.h> #define REP(i,m) for(int i=0;i<(m);++i) #define REPN(i,m,in) for(int i=(in);i<(m);++i) #define ALL(t) (t).begin(),(t).end() #define CLR(a) memset((a),0,sizeof(a)) #define pb push_back #define mp make_pair #define fr first #define sc second using namespace std; #ifdef DEB #define dump(x) cerr << #x << " = " << (x) << endl #define prl cerr<<"called:"<< __LINE__<<endl template<class T> void debug(T a,T b){ for(;a!=b;++a) cerr<<*a<<' ';cerr<<endl;} #else #define dump(x) ; #define prl ; template<class T> void debug(T a,T b){ ;} #endif template<class T> void chmin(T& a,const T& b) { if(a>b) a=b; } template<class T> void chmax(T& a,const T& b) { if(a<b) a=b; } typedef long long int lint; typedef pair<int,int> pi; namespace std{ template<class S,class T> ostream &operator <<(ostream& out,const pair<S,T>& a){ out<<'('<<a.fr<<','<<a.sc<<')'; return out; } } //const int INF=5e8; template<lint mod> struct Int_{ unsigned x; unsigned mpow(Int_ a,unsigned k){ Int_ res=1; while(k){ if(k&1) res=res*a; a=a*a; k>>=1; } return res.x; } unsigned inverse(Int_ a){ return mpow(a,mod-2); } Int_(): x(0) { } Int_(long long sig) { int sigt=sig%mod; if(sigt<0) sigt+=mod; x=sigt; } unsigned get() const { return (unsigned)x; } Int_ &operator+=(Int_ that) { if((x += that.x) >= mod) x -= mod; return *this; } Int_ &operator-=(Int_ that) { if((x += mod - that.x) >= mod) x -= mod; return *this; } Int_ &operator*=(Int_ that) { x = (unsigned long long)x * that.x % mod; return *this; } Int_ &operator=(Int_ that) { x=that.x; return *this;} Int_ &operator/=(Int_ that) { x=(unsigned long long) x * inverse(that.x)%mod; return *this;} bool operator==(Int_ that) const { return x==that.x; } bool operator!=(Int_ that) const { return x!=that.x; } Int_ operator-() const { return Int_(0)-Int_(*this);} Int_ operator+(Int_ that) const { return Int_(*this) += that; } Int_ operator-(Int_ that) const { return Int_(*this) -= that; } Int_ operator*(Int_ that) const { return Int_(*this) *= that; } Int_ operator/(Int_ that) const { return Int_(*this) /= that; } }; namespace std{ template<lint mod> ostream &operator <<(ostream& out,const Int_<mod>& a){ out<<a.get(); return out; } template<lint mod> istream &operator >>(istream& in,Int_<mod>& a){ in>>a.x; return in; } }; typedef Int_<1000000007> Int; Int dp[4005][4005]; Int comb[4005][4005]; pi ps[200005]; int n; int main(){ comb[0][0]=1; REP(i,4002) REP(j,4002){ comb[i+1][j]+=comb[i][j]; comb[i][j+1]+=comb[i][j]; } cin>>n; int M=2000; REP(i,n){ scanf("%d%d",&ps[i].fr,&ps[i].sc); dp[M-ps[i].fr][M-ps[i].sc].x++; } REP(i,4002) REP(j,4002){ dp[i+1][j]+=dp[i][j]; dp[i][j+1]+=dp[i][j]; } Int res=0; REP(i,n){ res+=dp[M+ps[i].fr][M+ps[i].sc]; } REP(i,n){ res-=comb[ps[i].fr*2][ps[i].sc*2]; } res/=2; cout<<res<<endl; return 0; }

codenet

s233921926

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; //#define cerr if (false) cerr #define db(x) cerr << #x << "=" << x << endl #define db2(x, y) cerr << #x << "=" << x << "," << #y << "=" << y << endl #define db3(x, y, z) cerr << #x << "=" << x << "," << #y << "=" << y << "," << #z << "=" << z << endl #define dbv(v) cerr << #v << "="; for (auto _x : v) cerr << _x << ", "; cerr << endl #define dba(a, n) cerr << #a << "="; for (int _i = 0; _i < (n); ++_i) cerr << a[_i] << ", "; cerr << endl template <typename A, typename B> ostream& operator<<(ostream& os, const pair<A, B>& x) { return os << "(" << x.first << "," << x.second << ")"; } typedef long long ll; typedef long double ld; const int MOD = 1000000007; struct Mint { int val; Mint() { val = 0; } Mint(const ll& x) { val = (-MOD <= x && x < MOD) ? x : x % MOD; if (val < 0) val += MOD; } friend bool operator==(const Mint& a, const Mint& b) { return a.val == b.val; } friend bool operator!=(const Mint& a, const Mint& b) { return !(a == b); } friend bool operator<(const Mint& a, const Mint& b) { return a.val < b.val; } Mint& operator+=(const Mint& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; } Mint& operator-=(const Mint& m) { if ((val -= m.val) < 0) val += MOD; return *this; } Mint& operator*=(const Mint& m) { val = (ll)val * m.val % MOD; return *this; } friend Mint modex(Mint a, ll p) { assert(p >= 0); Mint ans = 1; for (; p; p >>= 1, a *= a) if (p & 1) ans *= a; return ans; } Mint& operator/=(const Mint& m) { return *this *= modex(m, MOD - 2); } Mint& operator++() { return *this += 1; } Mint& operator--() { return *this -= 1; } Mint operator++(int) { Mint result(*this); *this += 1; return result; } Mint operator--(int) { Mint result(*this); *this -= 1; return result; } Mint operator-() const { return Mint(-val); } friend Mint operator+(Mint a, const Mint& b) { return a += b; } friend Mint operator-(Mint a, const Mint& b) { return a -= b; } friend Mint operator*(Mint a, const Mint& b) { return a *= b; } friend Mint operator/(Mint a, const Mint& b) { return a /= b; } friend ostream& operator<<(ostream& os, const Mint& x) { return os << x.val; } }; const int MAXN = 8005; Mint fac[MAXN], invfac[MAXN]; Mint binom(ll a, ll b) { if (b < 0) return 0; if (b > a) return 0; return fac[a] * invfac[b] * invfac[a - b]; } const int ZERO = 2000; Mint G[4005][4005]; int main() { fac[0] = 1; for (int i = 1; i < MAXN; ++i) fac[i] = fac[i - 1] * i; invfac[MAXN - 1] = 1 / fac[MAXN - 1]; for (int i = MAXN - 2; i >= 0; --i) invfac[i] = invfac[i + 1] * (i + 1); int n; scanf("%d", &n); vector<int> A(n), B(n); for (int i = 0; i < n; ++i) { scanf("%d%d", &A[i], &B[i]); G[ZERO - A[i]][ZERO - B[i]]++; } for (int a = 0; a < 4005; ++a) for (int b = 0; b < 4005; ++b) { if (a) G[a][b] += G[a - 1][b]; if (b) G[a][b] += G[a][b - 1]; } Mint ans = 0; for (int i = 0; i < n; ++i) { ans += G[A[i] + ZERO][B[i] + ZERO]; ans -= binom(2 * (A[i] + B[i]), 2 * A[i]); } ans /= 2; printf("%d\n", ans.val); }

codenet

s490969125

p04051

cpp

Accepted

#include <iostream> #include <sstream> #include <iomanip> #include <cstdio> #include <cstdlib> #include <cmath> #include <cctype> #include <cstring> #include <vector> #include <list> #include <queue> #include <deque> #include <stack> #include <map> #include <set> #include <algorithm> #include <iterator> #include <bitset> #include <ctime> #include <fstream> #include <complex> using namespace std; #define FOR(i,a,b) for(int i = (a); i <(b); i++) #define RFOR(i,b,a) for(int i = (b) - 1; i >= (a); i--) #define ITER(it,a) for(typeof(a.begin()) it = a.begin(); it != a.end(); it++) #define FILL(a, value) memset(a,value, sizeof(a)) #define ALL(a) a.begin(),a.end() #define SZ(a) (int)a.size() #define PB push_back #define MP make_pair typedef long long LL; typedef vector<LL> VI; typedef pair<int, LL> PII; const double PI = acos(-1.0); const int INF = 1000 * 1000 * 1000 + 7; const LL LINF = INF * (LL)INF; const int MOD = 1000 * 1000 * 1000 + 7; const int MAX = 1000 * 2 + 7; int F[MAX * 4], RF[MAX * 4]; PII A[200007]; int BP(LL a, int n) { LL res = 1; while(n) { if (n & 1)res = (res * a) % MOD; a *= a; a %= MOD; n >>= 1; } return res; } int C(int a, int b) { LL res = F[a]; res *= RF[b]; res %= MOD; res *= RF[a-b]; res %= MOD; return res; } int DP[2 * MAX][2 * MAX]; int get(int x, int y) { //cout << x << " " << y << endl; if (DP[x][y] != -1) { //if (DP[x][y])cout << x << " " << y << " " << DP[x][y] << endl; return DP[x][y]; } LL res = 0; if (x)res += get(x-1, y); if (y)res += get(x, y-1); while(res >= MOD)res -= MOD; return DP[x][y] = res; } int main() { //cout << f(2, 1) << endl; //freopen("input.txt", "r", stdin); //ios::sync_with_stdio(false);cin.tie(NULL); int n; scanf("%d", &n); FILL(DP, -1); RF[0] = F[0] = 1; FOR(i, 1, 4 * MAX) { F[i] = (F[i-1] * 1LL * i) % MOD; RF[i] = BP(F[i], MOD - 2); } int tot = 0; FOR(i, 0, n) { scanf("%d%d", &A[i].first, &A[i].second); int aa = -A[i].first + MAX; int bb = -A[i].second + MAX; // if (DP[aa][bb] == -1)DP[aa][bb] = 0; // DP[aa][bb]++; tot += C(2 * A[i].first + 2 * A[i].second, 2 * A[i].first); if (tot >= MOD)tot -= MOD; A[i].first = -A[i].first; A[i].second = -A[i].second; } LL ans = 0; sort(A, A + n); FOR(i, 0, n) { // cout << A[i].first << " " << A[i].second << endl; int aa = A[i].first + MAX, bb = A[i].second + MAX; get(aa, bb); DP[aa][bb]++; if (DP[aa][bb] >= MOD) DP[aa][bb] -= MOD; // cout << DP[A[i].first + MAX][A[i].second + MAX] << endl; } FOR(i, 0, n) { ans += get(-A[i].first + MAX, -A[i].second + MAX); if (ans >= MOD)ans -= MOD; } ans -= tot; if (ans < 0)ans += MOD; ans *= BP(2, MOD-2); ans %= MOD; printf("%lld\n", ans); return 0; }

codenet

s969408429

p04051

cpp

Accepted

//By TheOneYouWant #pragma GCC optimize ("-O2") #include <bits/stdc++.h> using namespace std; #define fastio ios_base::sync_with_stdio(0);cin.tie(0);cout.tie(0) #define pb push_back #define mp make_pair #define fi first #define se second #define all(x) x.begin(),x.end() #define memreset(a) memset(a,0,sizeof(a)) #define testcase(t) int t;cin>>t;while(t--) #define forstl(i,v) for(auto &i: v) #define forn(i,e) for(int i=0;i<e;++i) #define forsn(i,s,e) for(int i=s;i<e;++i) #define rforn(i,s) for(int i=s;i>=0;--i) #define rforsn(i,s,e) for(int i=s;i>=e;--i) #define bitcount(a) __builtin_popcount(a) // set bits (add ll) #define ln '\n' #define getcurrtime() cerr<<"Time = "<<((double)clock()/CLOCKS_PER_SEC)<<endl #define dbgarr(v,s,e) cerr<<#v<<" = "; forsn(i,s,e) cerr<<v[i]<<", "; cerr<<endl #define inputfile freopen("input.txt", "r", stdin) #define outputfile freopen("output.txt", "w", stdout) #define dbg(args...) { string _s = #args; replace(_s.begin(), _s.end(), ',', ' '); \ stringstream _ss(_s); istream_iterator<string> _it(_ss); err(_it, args); } void err(istream_iterator<string> it) { cerr<<endl; } template<typename T, typename... Args> void err(istream_iterator<string> it, T a, Args... args) { cerr << *it << " = " << a << "\t"; err(++it, args...); } template<typename T1,typename T2> ostream& operator <<(ostream& c,pair<T1,T2> &v){ c<<"("<<v.fi<<","<<v.se<<")"; return c; } template <template <class...> class TT, class ...T> ostream& operator<<(ostream& out,TT<T...>& c){ out<<"{ "; forstl(x,c) out<<x<<" "; out<<"}"; return out; } typedef long long ll; typedef unsigned long long ull; typedef long double ld; typedef pair<ll,ll> p64; typedef pair<int,int> p32; typedef pair<int,p32> p96; typedef vector<ll> v64; typedef vector<int> v32; typedef vector<v32> vv32; typedef vector<v64> vv64; typedef vector<p32> vp32; typedef vector<p64> vp64; typedef vector<vp32> vvp32; typedef map<int,int> m32; const int LIM=2e5+5,MOD=1e9+7; const ld EPS = 1e-9; mt19937 rng(chrono::steady_clock::now().time_since_epoch().count()); ll dp[4005][4005]; const ll SHIFT = 2002; const ll MAXN = 4005; ll fastpow (ll a, ll p){ if(p == 0) return 1; ll z = fastpow(a,p/2); z = (z*z)%MOD; if(p%2) z = (a*z)%MOD; return z; } int main(){ fastio; int n; cin>>n; vp32 v; forn(i,n){ int a,b; cin>>a>>b; v.pb(mp(a,b)); dp[SHIFT-a][SHIFT-b]++; } forn(i,MAXN-1){ forn(j,MAXN-1){ dp[i][j] %= MOD; dp[i+1][j] += dp[i][j]; dp[i][j+1] += dp[i][j]; } } ll ans = 0; forn(i,n){ ans += dp[SHIFT+v[i].fi][SHIFT+v[i].se]; ans %= MOD; } ll fact[LIM] = {0}; ll invfact[LIM] = {0}; fact[0] = 1; forsn(i,1,LIM) fact[i] = (fact[i-1]*i)%MOD; invfact[LIM-1] = fastpow(fact[LIM-1], MOD-2); rforn(i,LIM-2) invfact[i] = (invfact[i+1]*(i+1))%MOD; ll totsub = 0; forn(i,n){ ll a = v[i].fi, b = v[i].se; ll sub = fact[2*a+2*b]; sub = (sub * invfact[2*a])%MOD; sub = (sub * invfact[2*b])%MOD; totsub = (totsub+sub)%MOD; } ans -= totsub; ans %= MOD; if(ans < 0) ans += MOD; ans = (ans * invfact[2]) % MOD; cout<<ans<<ln; return 0; }

codenet

s578866402

p04051

cpp

Accepted

#include<iomanip> #include<limits> #include<thread> #include<utility> #include<iostream> #include<string> #include<algorithm> #include<set> #include<map> #include<vector> #include<stack> #include<queue> #include<cmath> #include<numeric> #include<cassert> #include<random> #include<chrono> #include<unordered_set> #include<unordered_map> #include<fstream> #include<list> #include<functional> #include<bitset> #include<complex> #include<tuple> using namespace std; typedef unsigned long long int ull; typedef long long int ll; typedef pair<ll,ll> pll; typedef pair<int,int> pi; typedef pair<double,double> pd; typedef pair<double,ll> pdl; #define F first #define S second const ll E=1e18+7; const ll MOD=1000000007; class comb{ private: ll mod; ll mx; vector<ll> F; vector<ll> FR; public: comb(ll mod=1000000007,ll mx=100000):mod(mod),mx(mx),F(mx+1,1),FR(mx+1,1){ mk_F(); } ll mod_pow(ll a,ll x){ a%=mod; ll ans=1; while(x>0){ if(x&1){ans*=a; ans%=mod;} a*=a; a%=mod; x>>=1; } return ans; } pll Ex_gcd(ll a,ll b){ if(b==0){return {1,0};} pll ret=Ex_gcd(b,a%b); ret.F-=a/b*ret.S; return {ret.S,ret.F}; } ll prime_R(ll a){ return mod_pow(a,mod-2); } ll R(ll a){ ll ret=Ex_gcd(a,mod).F; ret%=mod; if(ret<0){ret+=mod;} return ret; } void mk_F(){ for(ll i=1;i<=mx;i++){F[i]=F[i-1]*i%mod; FR[i]=R(F[i]);} } ll c(ll n,ll k){ if(n<k){return 0;} if(n==k || k==0){return 1;} return F[n]*FR[n-k]%mod*FR[k]%mod; } //mod must be prime ll Lucas_C(ll n,ll m){ ll ret=1; while(n>0 || m>0){ ret*=c(n%mod,m%mod); ret%=mod; n/=mod; m/=mod; } return ret; } ll Stirling(ll n,ll k){ ll ret=0; for(ll i=1;i<=k;i++){ if((k-i)%2){ret-=c(k,i)*mod_pow(i,n)%mod;} else{ret+=c(k,i)*mod_pow(i,n)%mod;} ret%=mod; } ret*=R(F[k]); ret%=mod; if(ret<0){ret+=mod;} return ret; } ll Bell(ll n,ll k){ ll ret=0; for(ll i=1;i<=k;i++){ret+=Stirling(n,i); ret%=mod;} return ret; } }; comb Comb; int main(){ ll n; cin>>n; const ll C=2100; vector<vector<ll>> A(2*C,vector<ll>(2*C,0)); vector<pll> p(n); for(int i=0;i<n;i++){ ll a,b; cin>>a>>b; A[C-a][C-b]++; p[i]={a,b}; } for(int i=0;i+1<2*C;i++){ for(int t=0;t+1<2*C;t++){ A[i][t]%=MOD; A[i+1][t]+=A[i][t]; A[i][t+1]+=A[i][t]; } } ll ans=0; for(int i=0;i<n;i++){ ans+=A[C+p[i].F][C+p[i].S]; } ans%=MOD; for(int i=0;i<n;i++){ ans-=Comb.c((p[i].F+p[i].S)*2,p[i].F*2); } ans%=MOD; ll inv=(MOD+1)/2; ans*=inv; ans%=MOD; if(ans<0){ans+=MOD;} cout<<ans<<endl; return 0; }

codenet

s403998366

p04051

cpp

Accepted

#include<bits/stdc++.h> using namespace std; #define ll int #define llu unsigned long long #define ld double #define llu unsigned long long #define rep(i,x,y) for(int i=int(x);i<int(y);++i) #define For(i,x,y) for(int i=int(x);i<=int(y);++i) #define FOr(i,x,y) for(int i=int(x);i>=int(y);--i) #define pi acos(-1) #define mk make_pair #define pa pair<ll,ll> #define lf else if #define IL inline #define max(x,y) ((x)<(y)?(y):(x)) #define min(x,y) ((x)<(y)?(x):(y)) #define sqr(x) ((x)*(x)) #define Mul(x,y) ((x)=1LL*(x)*(y)%mod) #define Add(x,y) ((x)=((x)+(y))%mod) #define Max(x,y) ((x)=((x)<(y)?(y):(x))) #define Min(x,y) ((x)=((x)>(y)?(y):(x))) #define E(x) return writeln(x),0 #define p(x) printf("~%lld~\n",LL(x)) #define pp(x,y) printf("~~%lld %lld~~\n",LL(x),LL(y)) #define LL (long long) #define ppp(x,y,z) printf("~~~%lld %lld %lld~~~\n",LL(x),LL(y),LL(z)) #define pppp(a,b,c,d) printf("~~~%lld %lld %lld %lld\n",LL(a),LL(b),LL(c),LL(d)) #define f_in(x) freopen(x".in","r",stdin) #define f_out(x) freopen(x".out","w",stdout) #define open(x) f_in(x),f_out(x) #define fi first #define se second #define GuYue puts("\nGuYueNa________________________________________________________________________________") typedef complex<double> E; namespace SHENZHEBEI{ #ifdef LOCAL struct _{_(){freopen("cf.in","r",stdin);}}_; #endif #define NEG 1 static const int GYN=2333333; char SZB[GYN],*S=SZB,*T=SZB; inline char gc(){ if (S==T){ T=(S=SZB)+fread(SZB,1,GYN,stdin); if (S==T) return '\n'; } return *S++; } #if NEG inline ll read(){ ll x=0,g=1; char ch=gc(); for (;!isdigit(ch);ch=gc()) if (ch=='-') g=-1; for (;isdigit(ch);ch=gc()) x=x*10-48+ch; return x*g; } inline void write(ll x){ if (x<0) putchar('-'),x=-x; if (x>=10) write(x/10); putchar(x%10+'0'); } #else inline ll read(){ ll x=0; char ch=gc(); for (;!isdigit(ch);ch=gc()); for (;isdigit(ch);ch=gc()) x=x*10-48+ch; return x; } inline void write(ll x){ if (x>=10) write(x/10); putchar(x%10+'0'); } #endif inline char readchar(){ char ch=gc(); for(;isspace(ch);ch=gc()); return ch; } inline ll readstr(char *s){ char ch=gc(); int cur=0; for(;isspace(ch);ch=gc()); for(;!isspace(ch);ch=gc()) s[cur++]=ch; s[cur]='\0'; return cur; } void Print(long long *a,int s,int t){For(i,s,t)printf("%lld ",a[i]);} void Print(int *a,int s,int t){For(i,s,t)printf("%d ",a[i]);} void Print(char *a,int s,int t){For(i,s,t)putchar(a[i]);} void writeln(ll x){write(x);puts("");} }using namespace SHENZHEBEI; const ll N=200100,mod=1e9+7; ll mp[4100][4100],a[N],b[N],n,cogito=2000,answ,c[4100][4100]; int main(){ For(i,0,cogito*2)For(j,0,cogito*2){ if (!i&&!j) c[i][j]=1; lf (!i) c[i][j]=c[i][j-1]; lf (!j) c[i][j]=c[i-1][j]; else c[i][j]=(c[i-1][j]+c[i][j-1])%mod; } n=read(); For(i,1,n)a[i]=read(),b[i]=read(),mp[-a[i]+cogito][-b[i]+cogito]++; For(i,0,2*cogito)For(j,0,2*cogito){ if(i)Add(mp[i][j],mp[i-1][j]); if(j)Add(mp[i][j],mp[i][j-1]); } For(i,1,n)Add(answ,mp[a[i]+cogito][b[i]+cogito]),Add(answ,-c[a[i]*2][b[i]*2]); writeln((1ll*answ*(mod+1)/2%mod+mod)%mod); }

codenet

s450503558

p04051

cpp

Accepted

#include <bits/stdc++.h> #include <unistd.h> using namespace std; #define DEBUG(x) cerr<<#x<<": "<<x<<endl; #define DEBUG_VEC(v) cerr<<#v<<":";for(int i=0;i<v.size();i++) cerr<<" "<<v[i]; cerr<<endl #define DEBUG_MAT(v) cerr<<#v<<endl;for(int i=0;i<v.size();i++){for(int j=0;j<v[i].size();j++) {cerr<<v[i][j]<<" ";}cerr<<endl;} typedef long long ll; #define vi vector<int> #define vl vector<ll> #define vii vector< vector<int> > #define vll vector< vector<ll> > #define vs vector<string> #define pii pair<int,int> #define pis pair<int,string> #define psi pair<string,int> #define pll pair<ll,ll> template<class S, class T> pair<S, T> operator+(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first + t.first, s.second + t.second); } template<class S, class T> pair<S, T> operator-(const pair<S, T> &s, const pair<S, T> &t) { return pair<S, T>(s.first - t.first, s.second - t.second); } template<class S, class T> ostream& operator<<(ostream& os, pair<S, T> p) { os << "(" << p.first << ", " << p.second << ")"; return os; } #define X first #define Y second #define rep(i,n) for(int i=0;i<(n);i++) #define rep1(i,n) for(int i=1;i<=(n);i++) #define rrep(i,n) for(int i=(n)-1;i>=0;i--) #define rrep1(i,n) for(int i=(n);i>0;i--) #define REP(i,a,b) for(int i=a;i<b;i++) #define in(x, a, b) (a <= x && x < b) #define all(c) c.begin(),c.end() template<class T> bool chmax(T &a, const T &b) { if (a<b) { a = b; return 1; } return 0; } template<class T> bool chmin(T &a, const T &b) { if (a>b) { a = b; return 1; } return 0; } #define UNIQUE(v) v.erase(std::unique(v.begin(), v.end()), v.end()); const ll inf = 1000000001; const ll INF = (ll)1e18 + 1; const ll MOD = 1000000007; //const ll MOD = 998244353; const double pi = 3.14159265358979323846; #define Sp(p) cout<<setprecision(15)<< fixed<<p<<endl; int dx[4] = { -1,0, 1,0 }, dy[4] = { 0,1,0,-1 }; int dx2[8] = { 1,1,0,-1,-1,-1,0,1 }, dy2[8] = { 0,1,1,1,0,-1,-1,-1 }; #define fio() cin.tie(0); ios::sync_with_stdio(false); // #define mp make_pair //#define endl '\n' const int m = 2000; ll dp[2*m + 1][2*m + 1]; const int MAXN = 10010; ll fact[MAXN]; ll rfact[MAXN]; ll mod_pow(ll x, ll p, ll M = MOD) { ll a = 1; while (p) { if (p % 2) a = a*x%M; x = x*x%M; p /= 2; } return a; } ll mod_inverse(ll a, ll M = MOD) { return mod_pow(a, M - 2, M); } void set_fact(ll n, ll M = MOD) { fact[0] = fact[1] = rfact[0] = rfact[1] = 1; for (ll i = 2; i <= n; i++) { fact[i] = i * fact[i - 1] % M; rfact[i] = mod_inverse(fact[i], M); } } int main() { set_fact(5*m); int n; cin >> n; vi a(n), b(n); rep (i, n) { cin >> a[i] >> b[i]; dp[m - a[i]][m - b[i]]++; } rep (i, 2*m + 1) { rep (j, 2*m + 1) { if (i > 0) { (dp[i][j] += dp[i - 1][j]) %= MOD; } if (j > 0) { (dp[i][j] += dp[i][j - 1]) %= MOD; } } } //DEBUG_MAT(dp); ll ans = 0; rep (idx, n) { int i = a[idx] + m, j = b[idx] + m; (ans += dp[i][j]) %= MOD; } rep (i, n) { ans -= fact[2*a[i] + 2*b[i]] * rfact[2*a[i]] % MOD * rfact[2*b[i]] % MOD; } ans %= MOD; ans = ans * mod_inverse(2) % MOD; ans = (ans + MOD) % MOD; cout << ans << endl; }

codenet

s153306452

p04051

cpp

Accepted

#include<iostream> #include<string> #include<cstdio> #include<vector> #include<cmath> #include<algorithm> #include<functional> #include<iomanip> #include<queue> #include<ciso646> #include<random> #include<map> #include<set> #include<bitset> #include<stack> #include<unordered_map> #include<utility> #include<cassert> #include<complex> using namespace std; //#define int long long typedef long long ll; typedef unsigned long long ul; typedef unsigned int ui; const ll mod = 1000000007; const ll INF = (1e+18) + 7; typedef pair<int, int>P; #define stop char nyaa;cin>>nyaa; #define rep(i,n) for(int i=0;i<n;i++) #define per(i,n) for(int i=n-1;i>=0;i--) #define Rep(i,sta,n) for(int i=sta;i<n;i++) #define rep1(i,n) for(int i=1;i<=n;i++) #define per1(i,n) for(int i=n;i>=1;i--) #define Rep1(i,sta,n) for(int i=sta;i<=n;i++) #define all(v) (v).begin(),(v).end() typedef pair<ll, ll> LP; typedef double ld; typedef pair<ld, ld> LDP; const ld eps = 1e-6; const ld pi = acos(-1.0); //typedef vector<vector<ll>> mat; typedef vector<int> vec; ll mod_pow(ll a, ll n) { ll res = 1; while (n) { if (n & 1)res = res * a%mod; a = a * a%mod; n >>= 1; } return res; } struct modint { ll n; modint() :n(0) { ; } modint(ll m) :n(m) { if (n >= mod)n %= mod; else if (n < 0)n = (n%mod + mod) % mod; } operator int() { return n; } }; bool operator==(modint a, modint b) { return a.n == b.n; } modint operator+=(modint &a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; } modint operator-=(modint &a, modint b) { a.n -= b.n; if (a.n < 0)a.n += mod; return a; } modint operator*=(modint &a, modint b) { a.n = ((ll)a.n*b.n) % mod; return a; } modint operator+(modint a, modint b) { return a += b; } modint operator-(modint a, modint b) { return a -= b; } modint operator*(modint a, modint b) { return a *= b; } modint operator^(modint a, int n) { if (n == 0)return modint(1); modint res = (a*a) ^ (n / 2); if (n % 2)res = res * a; return res; } ll inv(ll a, ll p) { return (a == 1 ? 1 : (1 - p * inv(p%a, a)) / a + p); } modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); } const int max_n = 1 << 20; modint fact[max_n], factinv[max_n]; void init() { fact[0] = modint(1); for (int i = 0; i < max_n - 1; i++) { fact[i + 1] = fact[i] * modint(i + 1); } factinv[max_n - 1] = modint(1) / fact[max_n - 1]; for (int i = max_n - 2; i >= 0; i--) { factinv[i] = factinv[i + 1] * modint(i + 1); } } modint comb(int a, int b) { if (a < 0 || b < 0 || a < b)return 0; return fact[a] * factinv[b] * factinv[a - b]; } int dx[4] = { 1,0,-1,0 }; int dy[4] = { 0,1,0,-1 }; modint dp[4002][4002]; void solve() { int n; cin >> n; vector<int> a(n), b(n); rep(i, n) { cin >> a[i] >> b[i]; dp[2000 - a[i]][2000 - b[i]] += 1; } rep(i, 4001)rep(j, 4001) { dp[i + 1][j] += dp[i][j]; dp[i][j + 1] += dp[i][j]; } modint ans = 0; rep(i, n) { ans -= comb(2 * a[i] + 2 * b[i], 2 * a[i]); ans += dp[2000 + a[i]][2000 + b[i]]; } ans = ans / (modint)2; cout << ans << endl; } signed main() { ios::sync_with_stdio(false); cin.tie(0); //expre(); //cout << fixed << setprecision(10); init(); //int t; cin >> t; rep(i, t)solve(); //while (cin >> n, n)solve(); solve(); stop return 0; }

codenet

s444964136

p04051

cpp

Accepted

#include<bits/stdc++.h> #define sqr(x) ((x)*(x)) #define ll long long #define ull unsigned long long #define ui unsigned int #define ld long double #define vi vector<int> #define HEAP(...) priority_queue<__VA_ARGS__ > #define heap(...) priority_queue<__VA_ARGS__,vector<__VA_ARGS__ >,greater<__VA_ARGS__ > > #define pii pair<int,int> #define pb push_back #define mp make_pair #define debuge cerr<<"isok"<<endl #define debug(x) cerr<<#x<<"="<<x<<endl #define dprintf(...) fprintf(stderr,__VA_ARGS__) #define SS second #define FF first #define ls (k<<1) #define rs (k<<1|1) #define clr(a,x) memset(a,x,sizeof(a)) #define cpy(a,x) memcpy(a,x,sizeof(a)) #define file(x) freopen(x".in","r",stdin),freopen(x".out","w",stdout) #define SZ(x) ((int)x.size()) using namespace std; template<class T> inline void gmin(T &x,const T &y){if(x>y) x=y;} template<class T> inline void gmax(T &x,const T &y){if(x<y) x=y;} const int BufferSize=1<<16; char buffer[BufferSize],*Bufferhead,*Buffertail; bool Terminal; inline char Getchar(){ if(Bufferhead==Buffertail){ int l=fread(buffer,1,BufferSize,stdin); if(!l){Terminal=1;return 0;} Buffertail=(Bufferhead=buffer)+l; } return *Bufferhead++; } template<class T>inline bool read(T &x){ x=0;char c=Getchar(),rev=0; while(c<'0'||c>'9'){rev|=c=='-';c=Getchar();if(Terminal)return 0;} while(c>='0'&&c<='9') x=x*10+c-'0',c=Getchar(); if(c=='.'){ c=Getchar();double t=0.1; while(c>='0'&&c<='9') x=x+(c-'0')*t,c=Getchar(),t=t/10; } x=rev?-x:x; return 1; } template<class T1,class T2> inline bool read(T1 &x,T2 &y){return read(x)&read(y);} template<class T1,class T2,class T3> inline bool read(T1 &x,T2 &y,T3 &z){return read(x)&read(y)&read(z);} template<class T1,class T2,class T3,class T4> inline bool read(T1 &x,T2 &y,T3 &z,T4 &w){return read(x)&read(y)&read(z)&read(w);} inline bool reads(char *x){ char c=Getchar(); while(c<33||c>126){c=Getchar();if(Terminal)return 0;} while(c>=33&&c<=126) (*x++)=c,c=Getchar(); *x=0;return 1; } template<class T>inline void print(T x,const char c='\n'){ if(!x){putchar('0');putchar(c);return;} if(x<0) putchar('-'),x=-x; int m=0,a[20]; while(x) a[m++]=x%10,x/=10; while(m--) putchar(a[m]+'0'); putchar(c); } //--------------------------------head--------------------------------------------- const int inf=0x3f3f3f3f; const int N=200005,M=100005,mod=1e9+7; template<class T,class S> inline void ch(T &x,const S y){x=(x+y)%mod;} inline int exp(int x,int y,const int mod=::mod){ int ans=1; while(y){ if(y&1) ans=(ll)ans*x%mod; x=(ll)x*x%mod;y>>=1; }return ans; } int n,ans,a[N],b[N]; int cnt[4005][4005],fac[8005],ifac[8005]; int main(){ #ifdef rqgao2014 freopen("input.txt","r",stdin); #endif read(n);fac[0]=1; for(int i=1;i<=8000;i++) fac[i]=(ll)fac[i-1]*i%mod; ifac[8000]=exp(fac[8000],mod-2); for(int i=8000;i;i--) ifac[i-1]=(ll)ifac[i]*i%mod; for(int i=1 ;i<=n;i++) read(a[i],b[i]),cnt[2000-a[i]][2000-b[i]]++; for(int i=0;i<=4000;i++) for(int j=0;j<=4000;j++) cnt[i][j]=((ll)cnt[i][j]+(i?cnt[i-1][j]:0)+(j?cnt[i][j-1]:0))%mod; for(int i=1;i<=n;i++) ch(ans,cnt[2000+a[i]][2000+b[i]]); for(int i=1;i<=n;i++) ch(ans,mod-(ll)fac[a[i]*2+b[i]*2]*ifac[a[i]*2]%mod*ifac[b[i]*2]%mod); print((ll)ans*(mod+1)/2%mod); return 0; }

codenet

s082359608

p04051

cpp

Accepted

/*{{{*/ #include <vector> #include <list> #include <map> #include <set> #include <queue> #include <deque> #include <stack> #include <bitset> #include <algorithm> #include <functional> #include <numeric> #include <utility> #include <sstream> #include <iostream> #include <iomanip> #include <cstdio> #include <cmath> #include <cstdlib> #include <ctime> #include <cstring> #include <unordered_map> #include <unordered_set> #include <cassert> using namespace std; typedef pair<int, int> PP; typedef long long LL; #define pb push_back #define fr first #define sc second #define bitcnt __builtin_popcount #define all(x) x.begin(), x.end() inline int ri() {int x; scanf("%d", &x); return x;} #define rep2(i, n, ...) for (int i = 0; i < (n); i ++) #define rep3(i, a, b, ...) for (int i = (a); i < (b); i ++) #define GET_MACRO(_1, _2, _3, NAME, ...) NAME #define rep(...) GET_MACRO(__VA_ARGS__, rep3, rep2)(__VA_ARGS__) #define drep2(i, n, ...) for (int i = (n) - 1; i >= 0; i --) #define drep3(i, a, b) for (int i = (a) - 1; i >= (b); i --) #define drep(...) GET_MACRO(__VA_ARGS__, drep3, drep2)(__VA_ARGS__) template<typename T>inline bool smax(T&a, T b){if(a<b){a=b;return true;}return false;} template<typename T>inline bool smin(T&a, T b){if(a>b){a=b;return true;}return false;} /*}}}*/ //mod int struct mint{ const static long long mod = 1e9 + 7; long long x; mint():x(0){} mint(long long x):x(((x%mod)+mod)%mod){}; mint operator+=(const mint&a){if((x+=a.x)>=mod) x-=mod; return *this;} mint operator-=(const mint&a){if((x+=mod-a.x)>=mod) x-=mod; return *this;} mint operator*=(const mint&a){(x*=a.x)%=mod; return *this;} mint operator*(const mint&a){return mint(*this)*=a;} mint operator-(const mint&a){return mint(*this)-=a;} mint operator+(const mint&a){return mint(*this)+=a;} template<typename T>mint operator*(const T&a){return mint(*this)*=a;} template<typename T>mint operator-(const T&a){return mint(*this)-=a;} template<typename T>mint operator+(const T&a){return mint(*this)+=a;} template<typename T>friend mint operator*(T x,const mint&m){return mint(x)*=m;} template<typename T>friend mint operator-(T x,const mint&m){return mint(x)-=m;} template<typename T>friend mint operator+(T x,const mint&m){return mint(x)+=m;} bool operator==(const mint& a)const{ return x == a.x;} operator long long () const {return x;} }; mint pw(mint a, long long b){mint res(1);while(b){if(b&1)res*=a;a*=a;b>>=1;}return res;} mint inv(mint a){return pw(a, mint::mod - 2);} //mod int const int maxn = 4010, base = 2001; mint p[maxn][maxn]; int n, a[200010], b[200010]; mint fac[maxn * 2], ifac[maxn * 2]; mint c(int a, int b) { return fac[a + b] * ifac[a] * ifac[b]; } int main() { #ifdef _TEST_ freopen("input.txt", "r", stdin); //freopen("out.txt", "w", stdout); #endif cin >> n; fac[0] = ifac[0] = 1; rep(i, 1, maxn * 2) fac[i] = fac[i - 1] * i, ifac[i] = ifac[i - 1] * inv(i); rep(i, n) { cin >> a[i] >> b[i]; p[base - a[i]][base - b[i]] += 1; } rep(i, 1, maxn) rep(j, 1, maxn) { p[i][j] += p[i - 1][j] + p[i][j - 1]; } mint res; rep(i, n) res += p[base + a[i]][base + b[i]]; rep(i, n) res -= c(2 * a[i], 2 * b[i]); cout << res * inv(2) << endl; return 0; }

codenet

s071249265

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; template <int MOD_> struct modnum { static constexpr int MOD = MOD_; static_assert(MOD_ > 0, "MOD must be positive"); private: using ll = long long; int v; static int minv(int a, int m) { a %= m; assert(a); return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a); } public: modnum() : v(0) {} modnum(ll v_) : v(int(v_ % MOD)) { if (v < 0) v += MOD; } explicit operator int() const { return v; } friend std::ostream& operator << (std::ostream& out, const modnum& n) { return out << int(n); } friend std::istream& operator >> (std::istream& in, modnum& n) { ll v_; in >> v_; n = modnum(v_); return in; } friend bool operator == (const modnum& a, const modnum& b) { return a.v == b.v; } friend bool operator != (const modnum& a, const modnum& b) { return a.v != b.v; } modnum inv() const { modnum res; res.v = minv(v, MOD); return res; } friend modnum inv(const modnum& m) { return m.inv(); } modnum neg() const { modnum res; res.v = v ? MOD-v : 0; return res; } friend modnum neg(const modnum& m) { return m.neg(); } modnum operator- () const { return neg(); } modnum operator+ () const { return modnum(*this); } modnum& operator ++ () { v ++; if (v == MOD) v = 0; return *this; } modnum& operator -- () { if (v == 0) v = MOD; v --; return *this; } modnum& operator += (const modnum& o) { v += o.v; if (v >= MOD) v -= MOD; return *this; } modnum& operator -= (const modnum& o) { v -= o.v; if (v < 0) v += MOD; return *this; } modnum& operator *= (const modnum& o) { v = int(ll(v) * ll(o.v) % MOD); return *this; } modnum& operator /= (const modnum& o) { return *this *= o.inv(); } friend modnum operator ++ (modnum& a, int) { modnum r = a; ++a; return r; } friend modnum operator -- (modnum& a, int) { modnum r = a; --a; return r; } friend modnum operator + (const modnum& a, const modnum& b) { return modnum(a) += b; } friend modnum operator - (const modnum& a, const modnum& b) { return modnum(a) -= b; } friend modnum operator * (const modnum& a, const modnum& b) { return modnum(a) *= b; } friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= b; } }; template <typename T> T pow(T a, long long b) { assert(b >= 0); T r = 1; while (b) { if (b & 1) r *= a; b >>= 1; a *= a; } return r; } using num = modnum<int(1e9) + 7>; vector<num> fact, ifact; void init(){ int N = 110000; fact = {1}; for(int i = 1; i < N; i++) fact.push_back(i * fact[i-1]); ifact.resize(N); ifact.back() = 1 / fact.back(); for(int i = N - 1; i > 0; i--) ifact[i-1] = i * ifact[i]; } num ncr(int n, int k){ if(k < 0 || k > n) return 0; return fact[n] * ifact[k] * ifact[n-k]; } num dp[4001][4001]; num collect[4001][4001]; int main(){ ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0); init(); num ans = 0; int n; cin >> n; for(int i = 0; i < n; i++){ int a, b; cin >> a >> b; ans -= ncr(2*a + 2*b, 2*a); dp[2000-a][2000-b] += 1; collect[2000+a][2000+b] += 1; } for(int i = 0; i <= 4000; i++){ for(int j = 0; j <= 4000; j++){ if(i) dp[i][j] += dp[i-1][j]; if(j) dp[i][j] += dp[i][j-1]; ans += collect[i][j] * dp[i][j]; } } ans /= 2; cout << ans << '\n'; }

codenet

s890930979

p04051

cpp

Accepted

#pragma GCC optimize("Ofast,fast-math,unroll-loops") #include <bits/stdc++.h> //#include <ext/pb_ds/assoc_container.hpp> //#include <ext/pb_ds/tree_policy.hpp> //#define int ll //#define double long double #define endl '\n' #define all(C) (C).begin(), (C).end() #define rall(C) (C).rbegin(), (C).rend() #define mp make_pair #define pb emplace_back #define dbg(x) cerr << #x << " : " << x << endl //#define PI 3.141592653589 using namespace std; //using namespace __gnu_pbds; using ll = long long; using ull = unsigned long long; using ld = long double; using pii = pair <int, int>; using pll = pair <ll, ll>; using pld = pair <ld, ld>; /* const ll MAX_MEM = 5e8; char MEM[MAX_MEM]; ll MEM_POS = 0; void* operator new(size_t x) { auto ret = MEM + MEM_POS; MEM_POS += x; assert(MEM_POS < MAX_MEM); return ret; } void operator delete(void*) {} */ template <class T> istream& operator>> (istream &in, vector <T> &a) { for (auto &i : a) in >> i; return in; } template <class T> ostream& operator<< (ostream &out, vector <T> a) { for (auto &i : a) out << i << ' '; return out; } template <class T, class U> istream& operator>> (istream &in, pair <T, U> &p) { in >> p.first >> p.second; return in; } template <class T, class U> ostream& operator<< (ostream &out, pair <T, U> p) { out << p.first << " " << p.second << " "; return out; } inline void Start() { ios_base::sync_with_stdio(0); cin.tie(0), cout.tie(0); //freopen("circlecover.in", "r", stdin); //freopen("circlecover.out", "w", stdout); } const int P = 1e9 + 7; int add(int a, int b) { return a + b >= P ? a + b - P : a + b; } int mul(int a, int b) { return ll(a) * b % P; } int bpow(int a, int n) { int res = 1; while (n) { if (n & 1) res = mul(res, a); a = mul(a, a); n >>= 1; } return res; } int rev(int x) { return bpow(x, P - 2); } int divi(int a, int b) { return mul(a, rev(b)); } int sub(int a, int b) { return add(a, P - b); } const int N = 2001; int _dp[2 * N][2 * N]; int _d[2 * N][2 * N]; int& dp(int i, int j) { return _dp[i + N][j + N]; } int& d(int i, int j) { return _d[i + N][j + N]; } const int INF = 1e9; signed main() { Start(); int n; cin >> n; vector <int> a(n), b(n); for (int i = 0; i < n; ++i) cin >> a[i] >> b[i]; for (int i = 0; i < 2 * N; ++i) for (int j = 0; j < 2 * N; ++j) _dp[i][j] = 0, _d[i][j] = INF; for (int i = 0; i < n; ++i) dp(-a[i], -b[i]) = add(dp(-a[i], -b[i]), 1); for (int i = 1; i < 2 * N; ++i) for (int j = 1; j < 2 * N; ++j) _dp[i][j] = add(_dp[i][j], add(_dp[i - 1][j], _dp[i][j - 1])); int sum = 0; for (int i = 0; i < n; ++i) sum = add(sum, dp(a[i], b[i])); vector <int> fact(4 * N, 1), revfact(4 * N, 1); for (int i = 1; i < 4 * N; ++i) fact[i] = mul(fact[i - 1], i), revfact[i] = divi(revfact[i - 1], i); for (int i = 0; i < n; ++i) sum = sub(sum, mul(fact[a[i] + b[i] + a[i] + b[i]], mul(revfact[a[i] + a[i]], revfact[b[i] + b[i]]))); sum = divi(sum, 2); cout << sum; return 0; }

codenet

s593086959

p04051

cpp

Accepted

/// {{{ Author: Wang, Yen-Jen // include #include <bits/stdc++.h> // using using namespace std; // types typedef long long ll; typedef pair<int,int> pii; // macro #define SZ(x) ((int)x.size()) #define ALL(x) (x).begin() , (x).end() #define REP(i , n) for(int i = 0; i < int(n); i++) #define REP1(i , a , b) for(int i = a; i <= int(b); i++) #define F first #define S second #define MP make_pair #define PB push_back #define LC o<<1 , l , m #define RC o<<1|1 , m + 1 , r #define MS(x , v) memset(x , (v) , sizeof(x)) // input inline bool SR(int &x) { return scanf("%d",&x) == 1; } inline bool SR(ll &x) { return scanf("%lld",&x) == 1; } inline bool SR(double &x) { return scanf("%lf",&x) == 1; } inline bool SR(char *s) { return scanf("%s",s) == 1; } inline bool RI() { return true; } template<typename I , typename... T> inline bool RI(I &x , T&... tail) { return SR(x) && RI(tail...); } // output inline void SP(const int x) { printf("%d",x); } inline void SP(const ll x) { printf("%lld",x); } inline void SP(const double x) { printf("%.16lf",x); } inline void SP(const char *s) { printf("%s",s); } inline void PL() { puts(""); } template<typename I , typename... T> inline void PL(const I x , const T... tail) { SP(x); if(sizeof...(tail)) putchar(' '); PL(tail...); } // debug #define WangYenJen #ifdef WangYenJen template<typename I> void _DOING(const char *s , I&& x) { cerr << s << " = " << x << endl; } template<typename I , typename... T> void _DOING(const char *s , I&& x , T&&... tail) { int c = 0; while(*s != ',' || c != 0) { if(*s == '(' || *s == '[' || *s == '{') c++; if(*s == ')' || *s == ']' || *s == '}') c--; cerr << *s++; } cerr << " = " << x << " , "; _DOING(s + 1 , tail...); } #define DEBUG(...) \ do {\ fprintf(stderr , "%s: Line %d - ",__PRETTY_FUNCTION__,__LINE__);\ _DOING(#__VA_ARGS__ , __VA_ARGS__);\ } while(0); #else #define DEBUG(...) #endif // constant number const int INF = 0x3f3f3f3f; const ll INF64 = 0x3f3f3f3f3f3f3f3fll; // random function inline int RAND() { static int x = 880301; return (x = x * 0xdefaced + 1) % 0x7fffffff; } /// }}} const ll MOD = 1000000000 + 7; const int MAX_N = 200000 + 7; const int MAX_X = 4000 + 7; const int DELTA = 2000; ll dp[MAX_X][MAX_X]; ll dp2[MAX_X][MAX_X]; int A[MAX_N], B[MAX_N]; ll power(ll a, ll n) { ll x = 1; while (n) { if (n & 1) x = x * a % MOD; a = a * a % MOD; n >>= 1; } return x; } ll inv(ll x) { return power(x, MOD - 2); } int main() { int N; RI(N); REP(i, N) { RI(A[i], B[i]); dp[-A[i] + DELTA][-B[i] + DELTA]++; } dp2[0][0] = 1; REP(i, MAX_X) { REP(j, MAX_X) { if (i) { dp[i][j] += dp[i - 1][j]; dp2[i][j] += dp2[i - 1][j]; if (dp[i][j] >= MOD) dp[i][j] -= MOD; if (dp2[i][j] >= MOD) dp2[i][j] -= MOD; } if (j) { dp[i][j] += dp[i][j - 1]; dp2[i][j] += dp2[i][j - 1]; if (dp[i][j] >= MOD) dp[i][j] -= MOD; if (dp2[i][j] >= MOD) dp2[i][j] -= MOD; } } } ll ans = 0; REP(i, N) { ans += dp[A[i] + DELTA][B[i] + DELTA]; if (ans >= MOD) ans -= MOD; ans -= dp2[A[i] * 2][B[i] * 2]; if (ans < 0) ans += MOD; } (ans *= inv(2)) %= MOD; PL(ans); return 0; }

codenet

s795450533

p04051

cpp

Accepted

/////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////// // _oo0oo_ // // o8888888o // // 88" . "88 ------ hzt1 // // (| -_- |) // // 0\ = /0 // // ___/`---'\___ // // .' \| |// '. // // / \||| : |||// \ // // / _||||| -:- |||||- \ // // | | \ - /// | | // // | \_| ''\---/'' |_/ | // // \ .-\__ '-' ___/-. / // // ___'. .' /--.--\ `. .'___ // // ."" '< `.___\_<|>_/___.' >' "". // // | | : `- \`.;`\ _ /`;.`/ - ` : | | // // \ \ `_. \_ __\ /__ _/ .-` / / // // =====`-.____`.___ \_____/___.-`___.-'===== // // `=---=' // // // // // // ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ // // // // God-He Bless All. // // This Code Will Never Explode. // // // // // /////////////////////////////////////////////////////////// /////////////////////////////////////////////////////////// #include<cstdio> #include<cstring> #include<cctype> #include<algorithm> #include<vector> #define pb push_back #define mp make_pair #define xx first #define yy second #define rep(i,a,b) for(int i=(a),i##_end_=(b);i<=i##_end_;i++) #define dwn(i,a,b) for(int i=(a),i##_end_=(b);i>=i##_end_;i--) using namespace std; const int Size=1<<16; char buffer[Size],*head,*tail; inline char Getchar() { if(head==tail) { int l=fread(buffer,1,Size,stdin); tail=(head=buffer)+l; } if(head==tail) return -1; return *head++; } inline int read() { int x=0,f=1;char c=Getchar(); for(;!isdigit(c);c=Getchar()) if(c=='-') f=-1; for(;isdigit(c);c=Getchar()) x=x*10+c-'0'; return x*f; } typedef long long ll; typedef pair<int,int> pii; const int maxn=200010; const int maxm=4010; const int mod=1000000007; const int inv2=500000004; int n,x[maxn],y[maxn]; int f[maxm][maxm]; int fac[maxn],ifac[maxn]; void init(int m) { ifac[0]=ifac[1]=fac[0]=1; rep(i,2,m*2) ifac[i]=(ll)(mod-mod/i)*ifac[mod%i]%mod; rep(i,1,m*2) ifac[i]=(ll)ifac[i-1]*ifac[i]%mod; rep(i,1,m*2) fac[i]=(ll)fac[i-1]*i%mod; rep(i,1,m) rep(j,1,m) (f[i][j]+=f[i-1][j])%=mod,(f[i][j]+=f[i][j-1])%=mod; } int main() { n=read(); rep(i,1,n) x[i]=read(),y[i]=read(),f[-x[i]+2001][-y[i]+2001]++; init(4002); int ans=0; rep(i,1,n) (ans+=f[x[i]+2001][y[i]+2001])%=mod; rep(i,1,n) (ans-=(ll)fac[x[i]*2+y[i]*2]*ifac[x[i]*2]%mod*ifac[y[i]*2]%mod)%=mod; (ans+=mod)%=mod; printf("%d\n",(ll)ans*inv2%mod); return 0; }

codenet

s914130935

p04051

cpp

Accepted

#include "bits/stdc++.h" using namespace std; #define rep(i,n) for(int (i)=0;(i)<(int)(n);++(i)) #define rer(i,l,u) for(int (i)=(int)(l);(i)<=(int)(u);++(i)) #define reu(i,l,u) for(int (i)=(int)(l);(i)<(int)(u);++(i)) static const int INF = 0x3f3f3f3f; static const long long INFL = 0x3f3f3f3f3f3f3f3fLL; typedef vector<int> vi; typedef pair<int, int> pii; typedef vector<pair<int, int> > vpii; typedef long long ll; template<typename T, typename U> static void amin(T &x, U y) { if(y < x) x = y; } template<typename T, typename U> static void amax(T &x, U y) { if(x < y) x = y; } template<int MOD> struct ModInt { static const int Mod = MOD; unsigned x; ModInt() : x(0) {} ModInt(signed sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } ModInt(signed long long sig) { int sigt = sig % MOD; if(sigt < 0) sigt += MOD; x = sigt; } int get() const { return (int)x; } ModInt &operator+=(ModInt that) { if((x += that.x) >= MOD) x -= MOD; return *this; } ModInt &operator-=(ModInt that) { if((x += MOD - that.x) >= MOD) x -= MOD; return *this; } ModInt &operator*=(ModInt that) { x = (unsigned long long)x * that.x % MOD; return *this; } ModInt &operator/=(ModInt that) { return *this *= that.inverse(); } ModInt operator+(ModInt that) const { return ModInt(*this) += that; } ModInt operator-(ModInt that) const { return ModInt(*this) -= that; } ModInt operator*(ModInt that) const { return ModInt(*this) *= that; } ModInt operator/(ModInt that) const { return ModInt(*this) /= that; } ModInt inverse() const { signed a = x, b = MOD, u = 1, v = 0; while(b) { signed t = a / b; a -= t * b; std::swap(a, b); u -= t * v; std::swap(u, v); } if(u < 0) u += Mod; ModInt res; res.x = (unsigned)u; return res; } bool operator==(ModInt that) const { return x == that.x; } bool operator!=(ModInt that) const { return x != that.x; } ModInt operator-() const { ModInt t; t.x = x == 0 ? 0 : Mod - x; return t; } }; template<int MOD> ModInt<MOD> operator^(ModInt<MOD> a, unsigned long long k) { ModInt<MOD> r = 1; while(k) { if(k & 1) r *= a; a *= a; k >>= 1; } return r; } typedef ModInt<1000000007> mint; vector<mint> fact, factinv; void nCr_computeFactinv(int N) { N = min(N, mint::Mod - 1); fact.resize(N + 1); factinv.resize(N + 1); fact[0] = 1; rer(i, 1, N) fact[i] = fact[i - 1] * i; factinv[N] = fact[N].inverse(); for(int i = N; i >= 1; i --) factinv[i - 1] = factinv[i] * i; } mint nCr(int n, int r) { if(n >= mint::Mod) return nCr(n % mint::Mod, r % mint::Mod) * nCr(n / mint::Mod, r / mint::Mod); return r > n ? 0 : fact[n] * factinv[n - r] * factinv[r]; } int main() { int N; while(~scanf("%d", &N)) { vector<int> A(N); vector<int> B(N); for(int i = 0; i < N; ++ i) scanf("%d%d", &A[i], &B[i]); int X = max(*max_element(A.begin(), A.end()), *max_element(B.begin(), B.end())) + 1; vector<vector<mint>> sum(X * 4 + 1, vector<mint>(X * 4 + 1)); rep(i, N) ++ sum[X * 2 - (A[i] + B[i])][X * 2 - A[i]].x; rep(i, X * 4) rep(j, X * 4) { mint x = sum[i][j]; if(x.x == 0) continue; sum[i + 1][j] += x; sum[i + 1][j + 1] += x; } nCr_computeFactinv(X * 4); mint ans; rep(i, N) { ans += sum[X * 2 + A[i] + B[i]][X * 2 + A[i]]; ans -= nCr((A[i] + B[i]) * 2, A[i] * 2); } ans /= 2; printf("%d\n", ans.get()); } return 0; }

codenet

s682231826

p04051

cpp

Accepted

# include <iostream> # include <algorithm> #include <array> # include <cassert> #include <cctype> #include <climits> #include <numeric> # include <vector> # include <string> # include <set> # include <map> # include <cmath> # include <iomanip> # include <functional> # include <tuple> # include <utility> # include <stack> # include <queue> # include <list> # include <bitset> # include <complex> # include <chrono> # include <random> # include <limits.h> # include <unordered_map> # include <unordered_set> # include <deque> # include <cstdio> # include <cstring> #include <stdio.h> #include<time.h> #include <stdlib.h> #include <cstdint> #include <cfenv> #include<fstream> //#include <bits/stdc++.h> using namespace std; using LL = long long; using ULL = unsigned long long; long long MOD = 1000000000 + 7; constexpr long long INF = numeric_limits<LL>::max(); const double PI = acos(-1); #define fir first #define sec second #define thi third #define debug(x) cerr<<#x<<": "<<x<<'\n' typedef pair<LL, LL> Pll; typedef pair<double, double> Dll; typedef pair<LL, pair<LL, LL>> Ppll; typedef pair<LL, pair<LL, bitset<100001>>> Pbll; typedef pair<LL, pair<LL, vector<LL>>> Pvll; typedef pair<LL, LL> Vec2; struct Tll { LL first, second, third; }; struct Fll { LL first, second, third, fourth; }; typedef pair<LL, Tll> Ptll; #define rep(i,rept) for(LL i=0;i<rept;i++) #define Rrep(i,mf) for(LL i=mf-1;i>=0;i--) LL h, w, n, m, k, t, s, p, q, last, first, cnt, sum, ans, dp[5000][5000],b[200000]; string str, ss; Pll a[210000]; bool f; char c; int di[4][2] = { { 0,1 },{ 1,0 },{ 0,-1 },{ -1,0 } }; struct Edge { LL to, cost; }; struct edge { LL from, to, cost; }; vector<LL>vec; vector<edge>ed; vector<LL>v; map<LL,LL>ma; set<LL>st; void YN(bool f) { if (f) cout << "YES" << endl; else cout << "NO" << endl; } void yn(bool f) { if (f) cout << "Yes" << endl; else cout << "No" << endl; } struct Combination { int mod; vector< int64_t > mfact, rfact; Combination(int sz, int mod) : mfact(sz + 1), rfact(sz + 1), mod(mod) { mfact[0] = 1; for (int i = 1; i < mfact.size(); i++) { mfact[i] = mfact[i - 1] * i % mod; } rfact[sz] = inv(mfact[sz]); for (int i = sz - 1; i >= 0; i--) { rfact[i] = rfact[i + 1] * (i + 1) % mod; } } int64_t fact(int k) const { return (mfact[k]); } int64_t pow(int64_t x, int64_t n) const { int64_t ret = 1; while (n > 0) { if (n & 1) (ret *= x) %= mod; (x *= x) %= mod; n >>= 1; } return (ret); } int64_t inv(int64_t x) const { return (pow(x, mod - 2)); } int64_t P(int n, int r) const { if (r < 0 || n < r) return (0); return (mfact[n] * rfact[n - r] % mod); } int64_t C(int p, int q) const { if (q < 0 || p < q) return (0); return (mfact[p] * rfact[q] % mod * rfact[p - q] % mod); } int64_t H(int n, int r) const { if (n < 0 || r < 0) return (0); return (r == 0 ? 1 : C(n + r - 1, r)); } }; Combination comb(10000,MOD); int main() { cin >> n; rep(i, n) { cin >> a[i].fir >> a[i].sec; dp[2000 - a[i].fir][2000 - a[i].sec] += 1; } rep(i, n) { sum += comb.C((a[i].fir + a[i].sec) * 2, a[i].fir * 2); sum %= MOD; } rep(i, 4100)rep(j, 4100) { dp[i + 1][j] += dp[i][j]; dp[i + 1][j] %= MOD; dp[i][j + 1] += dp[i][j]; dp[i][j + 1] %= MOD; } rep(i, n) { ans += dp[2000 + a[i].fir][2000 + a[i].sec]; ans %= MOD; } cout << ((ans - sum + MOD) % MOD)*comb.inv(2) % MOD << endl; return 0; }

codenet

s128712809

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin);i<(end);i++) #define REP(i, n) FOR(i,0,n) #define IFOR(i, begin, end) for(int i=(end)-1;i>=(begin);i--) #define IREP(i, n) IFOR(i,0,n) #define Sort(v) sort(v.begin(), v.end()) #define Reverse(v) reverse(v.begin(), v.end()) #define all(v) v.begin(),v.end() #define SZ(v) ((int)v.size()) #define Lower_bound(v, x) distance(v.begin(), lower_bound(v.begin(), v.end(), x)) #define Upper_bound(v, x) distance(v.begin(), upper_bound(v.begin(), v.end(), x)) #define Max(a, b) a = max(a, b) #define Min(a, b) a = min(a, b) #define bit(n) (1LL<<(n)) #define Ans(f, y, n) if(f) cout << y << endl; else cout << n << endl; #define debug(x) cout << #x << "=" << x << endl; #define vdebug(v) cout << #v << "=" << endl; REP(i, v.size()){ cout << v[i] << ","; } cout << endl; #define mdebug(m) cout << #m << "=" << endl; REP(i, m.size()){ REP(j, m[i].size()){ cout << m[i][j] << ","; } cout << endl;} #define pb push_back #define int long long #define INF 1000000000000000000 using vec = vector<int>; using mat = vector<vec>; using Pii = pair<int, int>; using PiP = pair<int, Pii>; using PPi = pair<Pii, int>; using bools = vector<bool>; using pairs = vector<Pii>; template<typename T> void readv(vector<T> &a){ REP(i, a.size()) cin >> a[i]; } void readv_m1(vector<int> &a){ REP(i, a.size()){cin >> a[i]; a[i]--;} } //int dx[4] = {1,0,-1,0}; //int dy[4] = {0,1,0,-1}; int mod = 1000000007; //int mod = 998244353; #define Add(x, y) x = (x + (y)) % mod #define Mult(x, y) x = (x * (y)) % mod #define AddMult(x, y, z) x = (x + (y) * (z)) % mod int modpow(int x, int n, int m){ int a = 1; IREP(i, 64){ a = (a * a) % m; if(((n >> i) & 1) == 1) a = (a * x) % m; } return a; } class Combination { public: vec fact, invfact; int MAX_N, mod; Combination(int MAX_N, int mod): MAX_N(MAX_N), mod(mod) { initialize(); } void initialize(){ fact = vec(MAX_N + 1); invfact = vec(MAX_N + 1); fact[0] = 1; FOR(i, 1, MAX_N + 1){ fact[i] = (fact[i - 1] * i) % mod; } invfact[MAX_N] = modpow(fact[MAX_N], mod - 2, mod); IREP(i, MAX_N){ invfact[i] = (invfact[i + 1] * (i + 1)) % mod; } } int nCr(int n, int r){ if(r > n || r < 0 || n < 0) return 0; if(n > MAX_N){ MAX_N = n; initialize(); } int a = fact[n]; a = (a * invfact[r]) % mod; a = (a * invfact[n - r]) % mod; return a; } int nPr(int n, int r){ if(r > n || r < 0 || n < 0) return 0; if(n > MAX_N){ MAX_N = n; initialize(); } int a = fact[n]; a = (a * invfact[n - r]) % mod; return a; } }; int dp[4001][4001] = {}; signed main(){ int N; cin >> N; vec A(N), B(N); REP(i, N){ cin >> A[i] >> B[i]; dp[2000 - A[i]][2000 - B[i]]++; } REP(i, 4001) REP(j, 4001){ if(i > 0) Add(dp[i][j], dp[i - 1][j]); if(j > 0) Add(dp[i][j], dp[i][j - 1]); } int ans = 0; REP(i, N) Add(ans, dp[2000 + A[i]][2000 + B[i]]); int x = 0; Combination C(5000, mod); REP(i, N) Add(x, C.nCr(2 * (A[i] + B[i]), 2 * A[i])); ans = (ans - x + mod) % mod; Mult(ans, modpow(2, mod - 2, mod)); cout << ans << endl; return 0; }

codenet

s812627743

p04051

cpp

Accepted

#include<stdio.h> #include<cstring> #include<cstdlib> #include<cmath> #include<iostream> #include<algorithm> #include<vector> #include<map> #include<set> #include<queue> #include<bitset> #include<utility> #include<functional> #include<iomanip> #include<sstream> #include<ctime> #include<cassert> using namespace std; #define y0 y0z #define y1 y1z #define yn ynz #define j0 j0z #define j1 j1z #define jn jnz #define tm tmz #define buli(x) (__builtin_popcountll(x)) #define bur0(x) (__builtin_ctzll(x)) #define bul2(x) (63-__builtin_clzll(x)) #define mp make_pair #define pb push_back #define fi first #define se second #define fil(a,b) memset((a),(b),sizeof(a)) #define cl(a) fil(a,0) #define siz(x) ((int)(x).size()) #define all(x) (x).begin(),(x).end() #define foreach(it,a) for(__typeof((a).begin()) it=(a).begin();it!=(a).end();it++) #define rep(i,a,b) for (int i=(a),_ed=(b);i<_ed;i++) #define per(i,a,b) for (int i=(b)-1,_ed=(a);i>=_ed;i--) #define pw(x) ((ll(1))<<(x)) #define upmo(a,b) (((a)=((a)+(b))%mo)<0?(a)+=mo:(a)) #define mmo(a,b) (((a)=1ll*(a)*(b)%mo)<0?(a)+=mo:(a)) void getre(){int x=0;printf("%d\n",1/x);} void gettle(){int res=1;while(1)res<<=1;printf("%d\n",res);} typedef pair<int,int> pii; typedef vector<int> vi; typedef vector<pii> vpii; template<typename T,typename S>inline bool upmin(T&a,const S&b){return a>b?a=b,1:0;} template<typename T,typename S>inline bool upmax(T&a,const S&b){return a<b?a=b,1:0;} template<typename N,typename PN>inline N flo(N a,PN b){return a>=0?a/b:-((-a-1)/b)-1;} template<typename N,typename PN>inline N cei(N a,PN b){return a>0?(a-1)/b+1:-(-a/b);} template<typename N>N gcd(N a,N b){return b?gcd(b,a%b):a;} template<typename N>inline int sgn(N a){return a>0?1:(a<0?-1:0);} #if ( ( _WIN32 || __WIN32__ ) && __cplusplus < 201103L) #define lld "%I64d" #else #define lld "%lld" #endif inline void gn(long long&x){ int sg=1;char c;while(((c=getchar())<'0'||c>'9')&&c!='-');c=='-'?(sg=-1,x=0):(x=c-'0'); while((c=getchar())>='0'&&c<='9')x=x*10+c-'0';x*=sg; } inline void gn(int&x){long long t;gn(t);x=t;} inline void gn(unsigned long long&x){long long t;gn(t);x=t;} inline void gn(double&x){double t;scanf("%lf",&t);x=t;} inline void gn(long double&x){double t;scanf("%lf",&t);x=t;} inline void gs(char *s){scanf("%s",s);} inline void gc(char &c){while((c=getchar())>126 || c<33);} inline void pc(char c){putchar(c);} #ifdef JCVB #define debug(...) fprintf(stderr, __VA_ARGS__) #else #define debug(...) #endif typedef long long ll; typedef double db; inline ll sqr(ll a){return a*a;} inline db sqrf(db a){return a*a;} const int inf=0x3f3f3f3f; const db pi=3.14159265358979323846264338327950288L; const db eps=1e-6; const int mo=1e9+7; int qp(int a,ll b){int n=1;do{if(b&1)n=1ll*n*a%mo;a=1ll*a*a%mo;}while(b>>=1);return n;} int f[4444][4444]; int Z=2100; int n; vpii pp; int fac[8888],ifac[8888]; int c(int a,int b){ int ans= 1ll*fac[a]*ifac[a-b]%mo*ifac[b]%mo; return ans; } int main() { #ifdef JCVB //freopen("1.in","r",stdin); //freopen("1.out","w",stdout); int _time_jc=clock(); #endif gn(n); fac[0]=1;rep(i,1,8300)fac[i]=1ll*fac[i-1]*i%mo; rep(i,0,8300)ifac[i]=qp(fac[i],mo-2); rep(i,1,n+1){ int x,y;gn(x);gn(y); pp.pb(mp(x,y)); f[Z-x][Z-y]++; } rep(i,1,4400)rep(j,1,4400)upmo(f[i][j],f[i-1][j]+f[i][j-1]); int su=0; rep(i,0,n) upmo(su,f[Z+pp[i].fi][Z+pp[i].se]); rep(i,0,n){ upmo(su,-c(2*pp[i].fi+2*pp[i].se,2*pp[i].fi)); } su=1ll*su*qp(2,mo-2)%mo; printf("%d\n",su); #ifdef JCVB debug("time: %d\n",int(clock()-_time_jc)); #endif return 0; }

codenet

s459812352

p04051

cpp

Accepted

// Copyright (C) 2017 __debug. // This program is free software; you can redistribute it and/or // modify it under the terms of the GNU General Public License as // published by the Free Software Foundation; version 3 // This program is distributed in the hope that it will be useful, // but WITHOUT ANY WARRANTY; without even the implied warranty of // MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the // GNU General Public License for more details. // You should have received a copy of the GNU General Public License // along with this program; If not, see <http://www.gnu.org/licenses/>. #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/priority_queue.hpp> #define x first #define y second #define MP std::make_pair #define SZ(x) ((int)(x).size()) #define ALL(x) (x).begin(), (x).end() #define DEBUG(...) fprintf(stderr, __VA_ARGS__) #ifdef __linux__ #define getchar getchar_unlocked #define putchar putchar_unlocked #endif using std::pair; using std::vector; using std::string; typedef long long LL; typedef pair<int, int> Pii; const int oo = 0x3f3f3f3f; template<typename T> inline bool chkmax(T &a, T b) { return a < b ? a = b, true : false; } template<typename T> inline bool chkmin(T &a, T b) { return b < a ? a = b, true : false; } string procStatus() { std::ifstream t("/proc/self/status"); return string(std::istreambuf_iterator<char>(t), std::istreambuf_iterator<char>()); } template<typename T> T read(T &x) { int f = 1; char ch = getchar(); for (; !isdigit(ch); ch = getchar()) f = (ch == '-' ? -1 : 1); for (x = 0; isdigit(ch); ch = getchar()) x = 10 * x + ch - '0'; return x *= f; } template<typename T> void write(T x) { if (x == 0) { putchar('0'); return; } if (x < 0) { putchar('-'); x = -x; } static char s[20]; int top = 0; for (; x; x /= 10) s[++top] = x % 10 + '0'; while (top) putchar(s[top--]); } // EOT const int MAXN = 2e5 + 5, RNG = 2e3 + 5; const int MOD = 1e9 + 7; int N; Pii A[MAXN]; void input() { read(N); for (int i = 1; i <= N; ++i) { read(A[i].x); read(A[i].y); } } int fac[RNG * 4], ifac[RNG * 4]; LL fpm(LL base, LL exp) { LL ret = 1; for (; exp; exp >>= 1) { if (exp & 1) (ret *= base) %= MOD; (base *= base) %= MOD; } return ret; } inline int C(int n, int k) { assert(0 <= k && k <= n); return (LL)fac[n] * ifac[k] % MOD * ifac[n - k] % MOD; } void solve() { fac[0] = 1; for (int i = 1; i < RNG * 4; ++i) { fac[i] = (LL)fac[i - 1] * i % MOD; } ifac[RNG * 4 - 1] = fpm(fac[RNG * 4 - 1], MOD - 2); for (int i = RNG * 4 - 1; i >= 1; --i) { ifac[i - 1] = (LL)ifac[i] * i % MOD; } static int dp[RNG * 2][RNG * 2]; static int cnt[RNG * 2][RNG * 2]; int ans = 0; for (int i = 1; i <= N; ++i) { dp[RNG - A[i].x][RNG - A[i].y] += 1; cnt[RNG + A[i].x][RNG + A[i].y] += 1; (ans += MOD - C(A[i].x * 2 + A[i].y * 2, A[i].x * 2)) %= MOD; } for (int i = 0; i < RNG * 2; ++i) { for (int j = 0; j < RNG * 2; ++j) { (dp[i][j] += (i ? dp[i - 1][j] : 0) + (j ? dp[i][j - 1] : 0)) %= MOD; (ans += (LL)cnt[i][j] * dp[i][j] % MOD) %= MOD; } } ans = (LL)ans * fpm(2, MOD - 2) % MOD; printf("%d\n", ans); } int main() { #ifdef __DEBUG freopen("E.in", "r", stdin); freopen("E.out", "w", stdout); #endif input(); solve(); return 0; } // 念兰堂红烛，心长焰短，向人垂泪。 // -- 晏殊《撼庭秋·别来音信千里》

codenet

s910085976

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define all(a)a.begin(),a.end() using ll=long long; const int INF = 1<<30; const ll INFll =1LL<<62; const int mod= int(1e9)+7; //const int mod=998244353; using P = pair<int,int>; using Pl= pair<ll,ll>; using ld=long double; using V=vector<int>; using Vl=vector<ll>; using VV=vector<vector<int>>; using VVl=vector<vector<ll>>; // modint: mod 計算を int を扱うように扱える構造体 template<int MOD> struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) val += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept { return os << x.val; } friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; using mint = Fp<mod>; const int MAX = 1001001; long long fac[MAX], finv[MAX], inv[MAX]; // テーブルを作る前処理 void COMinit() { fac[0] = fac[1] = 1; finv[0] = finv[1] = 1; inv[1] = 1; for (int i = 2; i < MAX; i++){ fac[i] = fac[i - 1] * i % mod; inv[i] = mod - inv[mod%i] * (mod / i) % mod; finv[i] = finv[i - 1] * inv[i] % mod; } } // 二項係数計算 long long COM(int n, int k){ if (n < k) return 0; if (n < 0 || k < 0) return 0; return fac[n] * (finv[k] * finv[n - k] % mod) % mod; } ll nPr(int n, int r) { if (n < 0 || r < 0 || n < r) return 0; return fac[n] * finv[n - r] % mod; } int main(){ COMinit(); ll n;cin>>n; V a(n),b(n),c(n); const int d=2000; VV memo(2*d+1,V()); for (int i = 0; i < n; ++i) { cin >>a[i]>>b[i]; c[i]=a[i]+b[i]; memo[c[i]].push_back(d-a[i]); } mint Y=0; for (int i = 0; i < n; ++i) { Y+=COM(2*c[i],2*a[i]); } // cout <<Y<<endl;//Y ok mint X=0; vector<mint>F(2*d+1,0); for (int i =2*d; i>=0 ;--i){ //*(1+x) auto nf=F; for (int j = 1; j <=2*d; ++j) { F[j]=nf[j]+nf[j-1]; } // +x^(d-a) if(memo[i].empty())continue; for(auto x:memo[i])F[x]+=1; } mint x=0; for (int i = 0; i <=2*d; ++i){ x+=F[i]*F[2*d-i]; } mint ans=x-Y; ans/=2; cout <<ans <<endl; }

codenet

s457683975

p04051

cpp

Accepted

#include <bits/stdc++.h> #define FOR(i,a,b) for( ll i = (a); i < (ll)(b); i++ ) #define REP(i,n) FOR(i,0,n) #define YYS(x,arr) for(auto& x:arr) #define ALL(x) (x).begin(),(x).end() #define SORT(x) sort( (x).begin(),(x).end() ) #define REVERSE(x) reverse( (x).begin(),(x).end() ) #define UNIQUE(x) (x).erase( unique( ALL( (x) ) ) , (x).end() ) #define PW(x) (1LL<<(x)) #define SZ(x) ((ll)(x).size()) #define SHOW(x) cout << #x << " = " << x << endl #define pb emplace_back #define fi first #define se second using namespace std; typedef long double ld; typedef long long int ll; typedef pair<int,int> pi; typedef pair<ll,ll> pl; typedef vector<int> vi; typedef vector<ll> vl; typedef vector<bool> vb; typedef vector<ld> vd; typedef vector<pi> vpi; typedef vector<pl> vpl; typedef vector<vpl> gr; typedef vector<vl> ml; typedef vector<vd> md; typedef vector<vi> mi; const ll INF = (ll)1e9 + 10; const ll INFLL = (ll)1e18 + 10; const ld EPS = 1e-12; const ll MOD = 1e9+7; template<class T> T &chmin( T &a , const T &b ){ return a = min(a,b); } template<class T> T &chmax( T &a , const T &b ){ return a = max(a,b); } template<class T> inline T sq( T a ){ return a * a; } ll in(){ ll x; scanf( "%lld" , &x ); return x; } char yuyushiki[1000010]; string stin(){ scanf( "%s" , yuyushiki ); return yuyushiki; } // head struct Mod{ unsigned n; Mod() : n(0){} Mod( ll x ){ if( x < 0 ) n = x%MOD+MOD; else n = x%MOD; } }; Mod operator + ( Mod a , Mod b ){ return Mod( a.n + b.n ); } Mod operator +=( Mod &a , Mod b ){ return a = a + b; } Mod operator - ( Mod a ){ return Mod( MOD - a.n ); } Mod operator - ( Mod a , Mod b ){ return Mod( a.n + MOD - b.n ); } Mod operator -=( Mod &a , Mod b ){ return a = a - b; } Mod operator * ( Mod a , Mod b ){ return Mod( (ll)a.n * b.n ); } Mod operator *=( Mod &a , Mod b ){ return a = a * b; } Mod modpow( Mod x , ll k ){ Mod res = 1; while( k ){ if( k & 1 ) res *= x; k /= 2; x *= x; } return res; } ll extgcd( ll a , ll b , ll &x , ll &y ){ ll d = a; if( b != 0 ){ d = extgcd( b , a % b , y , x ); y -= a / b * x; } else { x = 1, y = 0; } return d; } Mod inv( Mod a ){ ll x, y; assert( extgcd( a.n , MOD , x , y ) == 1 ); return Mod( x ); } Mod operator / ( Mod a , Mod b ){ return Mod( (ll)a.n * inv(b).n ); } Mod operator /=( Mod &a , Mod b ){ return a = a / b; } struct Factorial{ vector<Mod> v; Factorial( int max_n ){ v = vector<Mod>( max_n , 1 ); FOR( i , 1 , max_n ) v[i] = v[i-1] * i; } int size(){ return v.size(); } Mod operator [] ( int id ){ return v[id]; } }; struct Factorial_inv{ vector<Mod> v; Factorial_inv( Factorial &f ){ v = vector<Mod>( f.size() ); REP( i , f.size() ) v[i] = inv( f[i] ); } Mod operator [] ( int id ){ return v[id]; } }; struct Combination{ Factorial *f; Factorial_inv *finv; Combination( Factorial &arg_f , Factorial_inv &arg_finv ){ f = &arg_f; finv = &arg_finv; } Mod operator () ( int a , int b ){ return (*f)[a] * (*finv)[b] * (*finv)[a-b]; } }; Factorial fact( 1000010 ); Factorial_inv finv( fact ); Combination comb( fact , finv ); int n; int a[200010], b[200010]; Mod dp[4020*4020]; int p( int x , int y ){ x += 2010; y += 2010; return x * 4020 + y; } int main(){ n = in(); REP( i , n ){ a[i] = in(); b[i] = in(); dp[ p( -a[i] , -b[i] ) ] += 1; } FOR( i , -2005 , 2005 ){ FOR( j , -2005 , 2005 ){ dp[ p( i , j ) ] += dp[ p( i-1 , j ) ] + dp[ p( i , j-1 ) ]; } } Mod ans = 0; REP( i , n ){ ans += dp[ p( a[i] , b[i] ) ]; } REP( i , n ){ ans -= comb( 2 * ( a[i] + b[i] ) , 2 * a[i] ); } ans /= 2; cout << ans.n << endl; return 0; }

codenet

s814317345

p04051

cpp

Accepted

#include <cstdio> #include <algorithm> #include <stack> #include <queue> #include <deque> #include <vector> #include <string> #include <string.h> #include <cstdlib> #include <ctime> #include <cmath> #include <map> #include <set> #include <iostream> #include <sstream> #include <numeric> #include <cctype> #include <bitset> #include <cassert> #define fi first #define se second #define rep(i,n) for(int i = 0; i < (n); ++i) #define rrep(i,n) for(int i = 1; i <= (n); ++i) #define drep(i,n) for(int i = (n)-1; i >= 0; --i) #define gep(i,g,j) for(int i = g.head[j]; i != -1; i = g.e[i].next) #define each(it,c) for(__typeof((c).begin()) it=(c).begin();it!=(c).end();it++) #define rng(a) a.begin(),a.end() #define maxs(x,y) x = max(x,y) #define mins(x,y) x = min(x,y) #define pb push_back #define sz(x) (int)(x).size() #define pcnt __builtin_popcount #define uni(x) x.erase(unique(rng(x)),x.end()) #define snuke srand((unsigned)clock()+(unsigned)time(NULL)); #define df(x) int x = in() #define dame { puts("0"); return 0;} #define show(x) cout<<#x<<" = "<<x<<endl; using namespace std; typedef long long int ll; typedef pair<int,int> P; typedef vector<int> vi; typedef vector<vi> vvi; typedef vector<ll> vl; typedef vector<P> vp; inline int in() { int x; scanf("%d",&x); return x;} inline void priv(vi a) { rep(i,sz(a)) printf("%d%c",a[i],i==sz(a)-1?'\n':' ');} template<typename T>istream& operator>>(istream&i,vector<T>&v) {rep(j,sz(v))i>>v[j];return i;} template<typename T>string join(vector<T>&v) {stringstream s;rep(i,sz(v))s<<' '<<v[i];return s.str().substr(1);} template<typename T>ostream& operator<<(ostream&o,vector<T>&v) {if(sz(v))o<<join(v);return o;} template<typename T1,typename T2>istream& operator>>(istream&i,pair<T1,T2>&v) {return i>>v.fi>>v.se;} template<typename T1,typename T2>ostream& operator<<(ostream&o,pair<T1,T2>&v) {return o<<v.fi<<","<<v.se;} const int MX = 4005, C = 2002, INF = 1001001001; const ll LINF = 1e18; const double eps = 1e-10; // Mod int const int mod = 1000000007; struct mint; mint ex(mint a, ll tms); struct mint { ll x; mint():x(0){} mint(ll x):x((x%mod+mod)%mod){} // mint(ll x):x(x){} mint& fix() { x = (x%mod+mod)%mod; return *this;} mint& operator+=(const mint& a){ if((x+=a.x)>=mod) x-=mod; return *this;} mint& operator-=(const mint& a){ if((x+=mod-a.x)>=mod) x-=mod; return *this;} mint& operator*=(const mint& a){ (x*=a.x)%=mod; return *this;} mint& operator/=(const mint& a){ (x*=ex(a,mod-2).x)%=mod; return *this;} mint operator+(const mint& a)const{ return mint(*this) += a;} mint operator-(const mint& a)const{ return mint(*this) -= a;} mint operator*(const mint& a)const{ return mint(*this) *= a;} mint operator/(const mint& a)const{ return mint(*this) /= a;} bool operator<(const mint& a)const{ return x < a.x;} bool operator==(const mint& a)const{ return x == a.x;} }; istream& operator>>(istream&i,mint&a){i>>a.x;return i;} ostream& operator<<(ostream&o,const mint&a){o<<a.x;return o;} typedef vector<mint> vm; mint ex(mint a, ll tms) { if(!tms) return 1; mint res = ex(a,tms/2); res *= res; return (tms&1)?res*a:res; } struct comb { vm f, g; comb(){} comb(int mx):f(mx+1),g(mx+1) { f[0] = 1; rrep(i,mx) f[i] = f[i-1]*i; g[mx] = ex(f[mx],mod-2); for(int i=mx;i>0;i--) g[i-1] = g[i]*i; } mint c(int a, int b) { if (a < b) return 0; return f[a]*g[b]*g[a-b]; } }; // int main() { int n; scanf("%d",&n); vi a(n), b(n); rep(i,n) scanf("%d%d",&a[i],&b[i]); vector<vm> d(MX,vm(MX)); rep(i,n) d[C-a[i]][C-b[i]] += 1; rep(i,MX-1)rep(j,MX-1) d[i+1][j+1] += d[i][j+1]+d[i+1][j]; mint ans; rep(i,n) ans += d[C+a[i]][C+b[i]]; comb c(MX*2); rep(i,n) ans -= c.c(a[i]*2+b[i]*2,a[i]*2); ans /= 2; cout<<ans<<endl; return 0; }

codenet

s083289605

p04051

cpp

Accepted

/* #include <bits/stdc++.h> using namespace std; #define int long long const int MAXN = 2e5 + 10, INF = 1LL * 1e9 * 1e9; struct E{ int u, v, val; }edge[MAXN]; vector <int> adj[MAXN]; pair <int, int> p[MAXN][20]; bitset <MAXN> b; int dis[MAXN], h[MAXN]; pair <int, int> lca(int a, int b) { pair <int, int> res = {}; if (h[a] < h[b]) swap(a, b); int delta = h[a] - h[b]; int t = 0; for(;delta; delta >>= 1, ++t) if (delta & 1) { res.second = max(res.second, p[a][t].second); a = p[a][t].first; } t = 20 - 1; while(~(t--)) { if (p[a][t].first != p[b][t].first) { res.second = max(res.second, p[a][t].second); res.second = max(res.second, p[b][t].second); a = p[a][t].first; b = p[b][t].first; } } res.second =max(res.second, max(p[a][0].second, p[b][0].second)); res.first = p[a][0].first; return res; }// int32_t main () { ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); int n, m, sum = 0; cin >> n >> m; for (int i = 0; i < m; ++i) { cin >> edge[i].v >> edge[i].u >> edge[i].val; adj[edge[i].v].push_back(i); adj[edge[i].u].push_back(i); } set <pair <int, int>> s; for (int i = 1; i <= n; ++i) dis[i] = m; edge[m].val = INF; s.insert({0, 1}); while(!s.empty()) { auto now = *s.begin(); s.erase(now); int v = now.second, e = dis[v]; p[v][0] = {edge[e].v + edge[e].u - v, now.first}; sum += now.first; // cout << v << ' ' << sum << '\n'; h[v] = h[p[v][0].first] + 1; for (int i = 1; i < 20; ++i) p[v][i] = {p[p[v][i - 1].first][i - 1].first, max(p[p[v][i - 1].first][i - 1].second, p[v][i - 1].second)}; b[v] = true; for (auto i : adj[v]) { int u = edge[i].v + edge[i].u - v; if (!b[u] && edge[dis[u]].val > edge[i].val) { s.erase({edge[dis[u]].val, u}); dis[u] = i; s.insert({edge[dis[u]].val, u}); } } } for (int i = 0; i < m; ++i) cout << sum + edge[i].val - lca(edge[i].v, edge[i].u).second << '\n'; return 0; } /*/ #include <bits/stdc++.h> using namespace std; #define int long long const int MAXN = 2e5 + 10, MAX = 2010, md = 1e9 + 7; int dp[2 * MAX][2 * MAX], fact[4 * MAX], inv_fact[4 * MAX]; int combination(int k, int n) { if (k > n) return 0; return (fact[n] * inv_fact[k] % md) * inv_fact[n - k] % md; } int power(int n, int p) { int res = 1; for (;p; p >>= 1, n = n * n % md) if (p & 1) res = res * n % md; return res; } int a[MAXN], b[MAXN]; int32_t main () { fact[0] = 1; for (int i = 1; i < 4 * MAX; ++i) fact[i] = fact[i - 1] * i % md; inv_fact[4 * MAX - 1] = power(fact[4 * MAX - 1], md - 2); for (int i = 4 * MAX - 1; i; --i) inv_fact[i - 1] = inv_fact[i] * i % md; ios_base::sync_with_stdio(false), cin.tie(0), cout.tie(0); int n; cin >> n; for (int i = 0; i < n; ++i) cin >> a[i] >> b[i]; for (int i = 0; i < n; ++i) ++dp[MAX - a[i]][MAX - b[i]]; for (int i = 0; i < 2 * MAX - 1; ++i) for (int j = 0; j < 2 * MAX - 1; ++j) { dp[i + 1][j] += dp[i][j]; dp[i][j + 1] += dp[i][j]; if (dp[i + 1][j] >= md) dp[i + 1][j] %= md; if (dp[i][j + 1] >= md) dp[i][j + 1] %= md; } int ans = 0; for (int i = 0; i < n; ++i) { ans += (dp[MAX + a[i]][MAX + b[i]] + (md - 1) * combination(2 * a[i], 2 * b[i] + 2 * a[i])) % md; if (ans >= md) ans %= md; } cout << ans * power(2, md - 2) % md; return 0; }

codenet

s282044568

p04051

cpp

Accepted

#include<bits/stdc++.h> typedef unsigned int uint; typedef long long ll; typedef unsigned long long ull; typedef double lf; typedef long double llf; typedef std::pair<int,int> pii; #define xx first #define yy second template<typename T> inline T max(T a,T b){return a>b?a:b;} template<typename T> inline T min(T a,T b){return a<b?a:b;} template<typename T> inline T abs(T a){return a>0?a:-a;} template<typename T> inline bool repr(T &a,T b){return a<b?a=b,1:0;} template<typename T> inline bool repl(T &a,T b){return a>b?a=b,1:0;} template<typename T> inline T gcd(T a,T b){T t;if(a<b){while(a){t=a;a=b%a;b=t;}return b;}else{while(b){t=b;b=a%b;a=t;}return a;}} template<typename T> inline T sqr(T x){return x*x;} #define mp(a,b) std::make_pair(a,b) #define pb push_back #define I inline #define mset(a,b) memset(a,b,sizeof(a)) #define mcpy(a,b) memcpy(a,b,sizeof(a)) #define fo0(i,n) for(int i=0,i##end=n;i<i##end;i++) #define fo1(i,n) for(int i=1,i##end=n;i<=i##end;i++) #define fo(i,a,b) for(int i=a,i##end=b;i<=i##end;i++) #define fd0(i,n) for(int i=(n)-1;~i;i--) #define fd1(i,n) for(int i=n;i;i--) #define fd(i,a,b) for(int i=a,i##end=b;i>=i##end;i--) #define foe(i,x)for(__typeof(x.end())i=x.begin();i!=x.end();++i) struct Cg{I char operator()(){return getchar();}}; struct Cp{I void operator()(char x){putchar(x);}}; #define OP operator #define RT return *this; #define RX x=0;char t=P();while((t<'0'||t>'9')&&t!='-')t=P();bool f=0;\ if(t=='-')t=P(),f=1;x=t-'0';for(t=P();t>='0'&&t<='9';t=P())x=x*10+t-'0' #define RL if(t=='.'){lf u=0.1;for(t=P();t>='0'&&t<='9';t=P(),u*=0.1)x+=u*(t-'0');}if(f)x=-x #define RU x=0;char t=P();while(t<'0'||t>'9')t=P();x=t-'0';for(t=P();t>='0'&&t<='9';t=P())x=x*10+t-'0' #define TR *this,x;return x; I bool IS(char x){return x==10||x==13||x==' ';}template<typename T>struct Fr{T P;I Fr&OP,(int&x) {RX;if(f)x=-x;RT}I OP int(){int x;TR}I Fr&OP,(ll &x){RX;if(f)x=-x;RT}I OP ll(){ll x;TR}I Fr&OP,(char&x) {for(x=P();IS(x);x=P());RT}I OP char(){char x;TR}I Fr&OP,(char*x){char t=P();for(;IS(t);t=P());if(~t){for(;!IS (t)&&~t;t=P())*x++=t;}*x++=0;RT}I Fr&OP,(lf&x){RX;RL;RT}I OP lf(){lf x;TR}I Fr&OP,(llf&x){RX;RL;RT}I OP llf() {llf x;TR}I Fr&OP,(uint&x){RU;RT}I OP uint(){uint x;TR}I Fr&OP,(ull&x){RU;RT}I OP ull(){ull x;TR}};Fr<Cg>in; #define WI(S) if(x){if(x<0)P('-'),x=-x;char s[S],c=0;while(x)s[c++]=x%10+'0',x/=10;while(c--)P(s[c]);}else P('0') #define WL if(y){lf t=0.5;for(int i=y;i--;)t*=0.1;if(x>=0)x+=t;else x-=t,P('-');*this,(ll)(abs(x));P('.');if(x<0)\ x=-x;while(y--){x*=10;x-=floor(x*0.1)*10;P(((int)x)%10+'0');}}else if(x>=0)*this,(ll)(x+0.5);else *this,(ll)(x-0.5); #define WU(S) if(x){char s[S],c=0;while(x)s[c++]=x%10+'0',x/=10;while(c--)P(s[c]);}else P('0') template<typename T>struct Fw{T P;I Fw&OP,(int x){WI(10);RT}I Fw&OP()(int x){WI(10);RT}I Fw&OP,(uint x){WU(10);RT} I Fw&OP()(uint x){WU(10);RT}I Fw&OP,(ll x){WI(19);RT}I Fw&OP()(ll x){WI(19);RT}I Fw&OP,(ull x){WU(20);RT}I Fw&OP() (ull x){WU(20);RT}I Fw&OP,(char x){P(x);RT}I Fw&OP()(char x){P(x);RT}I Fw&OP,(const char*x){while(*x)P(*x++);RT} I Fw&OP()(const char*x){while(*x)P(*x++);RT}I Fw&OP()(lf x,int y){WL;RT}I Fw&OP()(llf x,int y){WL;RT}};Fw<Cp>out; const int N=200007,M=4007,P=1000000007; int n,a[N],b[N],fac[M*2],fin[M*2],f[M*2][M*2]; inline int pow(int a,int b) { int r=1; for(;b;b>>=1,a=(ll)a*a%P) if(b&1)r=(ll)r*a%P; return r; } inline int C(int a,int b) { return(ll)fac[a+b]*fin[a]%P*fin[b]%P; } int main() { fac[0]=1; fo1(i,M*2-1)fac[i]=(ll)fac[i-1]*i%P; fin[M*2-1]=pow(fac[M*2-1],P-2); fd1(i,M*2-1)fin[i-1]=(ll)fin[i]*i%P; in,n; fo1(i,n)in,a[i],b[i]; fo1(i,n)f[M-a[i]][M-b[i]]++; fo1(i,M*2-1)fo1(j,M*2-1)(f[i][j]+=f[i-1][j]+f[i][j-1])%=P; int ans=0; fo1(i,n)(ans+=f[M+a[i]][M+b[i]])%=P; fo1(i,n)(ans+=P-C(a[i]*2,b[i]*2))%=P; ans=(ll)ans*(P+1)/2%P; out,ans,'\n'; }

codenet

s691835546

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define rep(i, n) for(int i = 0; i < n; i++) #define rep2(i, x, n) for(int i = x; i <= n; i++) #define rep3(i, x, n) for(int i = x; i >= n; i--) #define elif else if #define sp(x) fixed << setprecision(x) #define pb push_back #define eb emplace_back #define all(x) x.begin(), x.end() #define sz(x) (int)x.size() using ll = long long; using pii = pair<int, int>; using pil = pair<int, ll>; using pli = pair<ll, int>; using pll = pair<ll, ll>; const ll MOD = 1000000007; //const ll MOD = 998244353; const int inf = (1<<30)-1; const ll INF = (1LL<<60)-1; const double pi = acos(-1.0); const double EPS = 1e-10; template<typename T> bool chmax(T &x, const T &y) {return (x < y)? (x = y, true) : false;}; template<typename T> bool chmin(T &x, const T &y) {return (x > y)? (x = y, true) : false;}; template<ll mod> struct Mod_Int{ ll x; Mod_Int() {} Mod_Int(ll y) : x (y >= 0 ? y % mod : (mod - (-y) % mod) % mod) {} Mod_Int &operator += (const Mod_Int &p){ x = (x + p.x) % mod; return *this; } Mod_Int &operator -= (const Mod_Int &p){ x = (x + mod - p.x) % mod; return *this; } Mod_Int &operator *= (const Mod_Int &p){ x = (x * p.x) % mod; return *this; } Mod_Int &operator /= (const Mod_Int &p){ *this *= p.inverse(); return *this; } Mod_Int &operator ++ () {return *this += Mod_Int(1);} Mod_Int operator ++ (int){ Mod_Int tmp = *this; ++*this; return tmp; } Mod_Int &operator -- () {return *this -= Mod_Int(1);} Mod_Int operator -- (int){ Mod_Int tmp = *this; --*this; return tmp; } Mod_Int operator - () const {return Mod_Int(-x);} Mod_Int operator + (const Mod_Int &p) const {return Mod_Int(*this) += p;} Mod_Int operator - (const Mod_Int &p) const {return Mod_Int(*this) -= p;} Mod_Int operator * (const Mod_Int &p) const {return Mod_Int(*this) *= p;} Mod_Int operator / (const Mod_Int &p) const {return Mod_Int(*this) /= p;} bool operator == (const Mod_Int &p) const {return x == p.x;} bool operator != (const Mod_Int &p) const {return x != p.x;} Mod_Int inverse() const { assert(*this != Mod_Int(0)); return pow(mod-2); } Mod_Int pow(ll k) const{ Mod_Int now = *this, ret = 1; while(k){ if(k&1) ret *= now; now *= now, k >>= 1; } return ret; } friend ostream &operator << (ostream &os, const Mod_Int &p){ return os << p.x; } friend istream &operator >> (istream &is, Mod_Int &p){ ll a; is >> a; p = Mod_Int<mod>(a); return is; } }; using mint = Mod_Int<MOD>; template<typename T> struct combination{ vector<T> _fac, _ifac; combination(int n){ _fac.resize(n+1), _ifac.resize(n+1); _fac[0] = 1; rep2(i, 1, n) _fac[i] = _fac[i-1]*i; _ifac[n] = _fac[n].inverse(); rep3(i, n, 1) _ifac[i-1] = _ifac[i]*i; } T fac(int k) const {return _fac[k];} T ifac(int k) const {return _ifac[k];} T comb(int n, int k) const{ if(k < 0 || n < k) return 0; return fac(n) * ifac(n-k) * ifac(k); } T perm(int n, int k) const{ if(k < 0 || n < k) return 0; return fac(n) * ifac(n-k); } }; int main(){ int N; cin >> N; mint dp[4002][4002]; fill(dp[0], dp[4002], 0); mint ans = 0; combination<mint> c(10000); int a[N], b[N]; rep(i, N){ cin >> a[i] >> b[i]; dp[2000-a[i]][2000-b[i]]++; ans -= c.comb(2*(a[i]+b[i]), 2*a[i]); } rep2(i, 0, 4000){ rep2(j, 0, 4000){ dp[i+1][j] += dp[i][j], dp[i][j+1] += dp[i][j]; } } rep(i, N) ans += dp[2000+a[i]][2000+b[i]]; cout << ans/2 << endl; }

codenet

s056543382

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; using lint = long long int; using pint = pair<int, int>; using plint = pair<lint, lint>; struct fast_ios { fast_ios(){ cin.tie(0); ios::sync_with_stdio(false); cout << fixed << setprecision(20); }; } fast_ios_; #define FOR(i, begin, end) for(int i=(begin),i##_end_=(end);i<i##_end_;i++) #define IFOR(i, begin, end) for(int i=(end)-1,i##_begin_=(begin);i>=i##_begin_;i--) #define REP(i, n) FOR(i,0,n) #define IREP(i, n) IFOR(i,0,n) template<typename T> istream &operator>>(istream &is, vector<T> &vec){ for (auto &v : vec) is >> v; return is; } template<typename T> ostream &operator<<(ostream &os, const vector<T> &vec){ os << "["; for (auto v : vec) os << v << ","; os << "]"; return os; } template<typename T> ostream &operator<<(ostream &os, const deque<T> &vec){ os << "deq["; for (auto v : vec) os << v << ","; os << "]"; return os; } template<typename T> ostream &operator<<(ostream &os, const set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template<typename T> ostream &operator<<(ostream &os, const unordered_set<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template<typename T> ostream &operator<<(ostream &os, const multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template<typename T> ostream &operator<<(ostream &os, const unordered_multiset<T> &vec){ os << "{"; for (auto v : vec) os << v << ","; os << "}"; return os; } template<typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &pa){ os << "(" << pa.first << "," << pa.second << ")"; return os; } template<typename TK, typename TV> ostream &operator<<(ostream &os, const map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } template<typename TK, typename TV> ostream &operator<<(ostream &os, const unordered_map<TK, TV> &mp){ os << "{"; for (auto v : mp) os << v.first << "=>" << v.second << ","; os << "}"; return os; } template<typename T> void ndarray(vector<T> &vec, int len) { vec.resize(len); } template<typename T, typename... Args> void ndarray(vector<T> &vec, int len, Args... args) { vec.resize(len); for (auto &v : vec) ndarray(v, args...); } template<typename T> void Max(T &m, const T q) { if (m < q) m = q; } template<typename T> void Min(T &m, const T q) { if (m > q) m = q; } template<typename T1, typename T2> pair<T1, T2> operator+(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first + r.first, l.second + r.second); } template<typename T1, typename T2> pair<T1, T2> operator-(pair<T1, T2> &l, pair<T1, T2> &r) { return make_pair(l.first - r.first, l.second - r.second); } #define dbg(x) cerr << #x << " = " << (x) << " (L" << __LINE__ << ") " << __FILE__ << endl; constexpr int zero = 2001; constexpr lint MDO = 1000000007; vector<vector<lint>> dp; constexpr lint MOD = 1000000007; vector<lint> fac, facInv, inv; void facInit(int nmax) { fac = facInv = inv = vector<lint>(nmax + 1, 1); for (int i = 2; i <= nmax; i++) { fac[i] = fac[i-1] * i % MOD; inv[i] = MOD - inv[MOD%i] * (MOD/i) % MOD; facInv[i] = facInv[i-1] * inv[i] % MOD; } } lint nCr(int n, int r) { if (n<r || r<0) return 0; if (n >= (int)fac.size()) facInit(n); return (fac[n] * facInv[r] % MOD) * facInv[n-r] % MOD; } int main() { int N; cin >> N; vector<pint> AB(N); REP(i, N) cin >> AB[i].first >> AB[i].second; ndarray(dp, zero * 2 + 1, zero * 2 + 1); REP(i, N) dp[zero - AB[i].first][zero - AB[i].second]++; REP(i, zero * 2) REP(j, zero * 2) { if (i) dp[i][j] += dp[i - 1][j]; if (j) dp[i][j] += dp[i][j - 1]; dp[i][j] %= MOD; } facInit(8000); lint ans = 0; REP(i, N) ans += dp[zero + AB[i].first][zero + AB[i].second]; REP(i, N) ans += MOD - nCr((AB[i].first + AB[i].second) * 2, AB[i].first * 2); ans = ans % MOD * ((1 + MOD) / 2) % MOD; cout << ans << endl; }

codenet

s367874621

p04051

cpp

Accepted

#include "bits/stdc++.h" #define YES "YES" #define NO "NO" #define YESNO OUT(three(solve(),YES,NO)) #define ECHO OUT(solve()) #define three(A,B,C) ((A)?(B):(C)) #define FOR(i,a,b) for(LL i=(a);i< (LL)(b);i++) #define EFOR(i,a,b) for(LL i=(a);i<=(LL)(b);i++) #define RFOR(i,a,b) for(LL i=(b);i>=(LL)(a);i--) #define REP(i,b) FOR(i,zero,b) #define EREP(i,b) EFOR(i,zero,b) #define RREP(i,b) RFOR(i,b,zero) #define ALL(c) c.begin(),c.end() #define UNIQUE(c) sort(ALL(c));c.erase(unique(ALL(c)),c.end()) #define MAX(c) (*max_element(ALL(c))) #define MIN(c) (*min_element(ALL(c))) #define MP make_pair #define FI first #define SE second #define SI(x) (LL(x.size())) #define PB push_back #define DEBUG(a) OUT(a) #define DEBUG2(a,b) OUT2(a,b) #define cat cout << __LINE__ << endl #define OUT(a) cout << (a) << endl #define OUT2(a,b) cout << (a) <<" "<<(b) << endl #define zero 0LL #define int long long #define pb emplace_back #define eb pb using namespace std; template<typename T> inline void maximize(T &a, T b) { a = max(a, b); } template<typename T> inline void minimize(T &a, T b) { a = min(a, b); } template<typename T> inline bool middle(T a, T b, T c) { return b <= a && a <= c; } template<class T> inline bool MX(T &l, const T &r) { return l < r ? l = r, 1 : 0; } template<class T> inline bool MN(T &l, const T &r) { return l > r ? l = r, 1 : 0; } typedef int LL; typedef double ld; typedef int ut; typedef vector<ut> VI; typedef vector<VI> VII; typedef pair<ut, ut> pr; typedef pair<ut, pr> ppr; typedef vector<pr> Vpr; typedef vector<ppr> Vppr; typedef tuple<int, int, int, int> tapu; typedef vector<tapu> Vtapu; typedef priority_queue<tapu, Vtapu, greater<tapu> > PQ; inline void outputVI(VI x) { REP(i, SI(x)) { cout << three(i, " ", "") << x[i]; }OUT(""); } const int SIZE1 = 2e5 + 1000; const int SIZE2 = 2010; const int SIZE3 = 430; const int SIZE = SIZE1; const int MAPSIZE = 40; const LL p = 7 + 1e9; const LL INF = 1LL << 60; const long double EPS = 1e-7; typedef pair<ld, ut> pld; #define endl "\n" //インタラクティブでは消す //ut A,B,C,D,E,F,G,H,I,J,O,P,Q,R,T,U; ut N, M, K, L, Q, D, H, W; VI edges[SIZE]; LL vals[SIZE], maps2[SIZE2][SIZE2], answer = zero; LL maps[SIZE2][SIZE2]; int A[SIZE],B[SIZE]; LL times[SIZE2][SIZE2]; LL fact[SIZE], gyaku[SIZE]; inline LL nCr(LL n, LL r) { return fact[n] * gyaku[n - r]%p * gyaku[r]%p; } inline LL twin(LL a1, LL b1, LL a2, LL b2) { return nCr(a1 + b1 + a2 + b2, a1 + a2); } LL modpow(LL n, LL r) { if (r == 0) return 1; LL ans = modpow(n*n%p, r / 2); if (r % 2) ans *= n; return ans % p; } LL rev(LL x) { return modpow(x, p - 2); } LL solve() { cin >> N; fact[0] = 1; gyaku[0] = 1; EFOR(i, 1, SIZE2 * 4) fact[i] = fact[i - 1] * i%p; EFOR(i, 1, SIZE2*4) gyaku[i] = gyaku[i - 1] * rev(i)%p; // cout << nCr(8000, 4000) << endl; REP(i, N) { cin >> A[i] >> B[i]; times[A[i]][B[i]]++; } LL ans = 0; RFOR(i,0,SIZE2*2) { // cout << i << endl; REP(a, i) { LL b = i - a; if (max(a, b) >= SIZE2) continue; if (a <= 0 or b <= 0) continue; times[a-1][b] += times[a][b]; times[a][b - 1] += times[a][b]; times[a - 1][b] %= p; times[a][b - 1] %= p; ans -= twin(a, b - 1, a - 1, b)*times[a][b]%p; ans += p; times[a][b] = 0; ans %= p; } } LL ansc = 0; REP(i, SIZE2) REP(j, SIZE2) { if (i == j) continue; LL resa = twin(i, 0, j, 0); LL resb = twin(i, 0, 0, j); ansc += resa*times[i][0]%p*times[j][0]%p; ansc += resb*times[i][0]%p*times[0][j]%p; ansc += resb*times[0][i]%p*times[j][0]%p; ansc += resa*times[0][i]%p*times[0][j]%p; ansc %= p; } ans += gyaku[2] % p*ansc; // cout << "OK" << endl; REP(i, SIZE2){ ans += twin(i, 0, i, 0) % p*(times[i][0]*(times[i][0]-1)/2) % p; ans += twin(0, i, 0, i) % p*(times[0][i]*(times[0][i]-1)/2) % p; ans += twin(i, 0, 0, i) % p*times[i][0] % p*(times[0][i]) % p; ans %= p; } cout << ans << endl; return 0; } //!!!!!!!!!!!!!!!!!!!実装を詰める!!!!!!!!!!!!!!!!!!!!!!!!! signed main() { ios_base::sync_with_stdio(false); cout << fixed << setprecision(0); solve(); cin >> N; return 0; }

codenet

s720340688

p04051

cpp

Accepted

// includes #include <bits/stdc++.h> using namespace std; // macros #define pb emplace_back #define mk make_pair #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define whole(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define bit(n) (1LL<<(n)) // functions template <typename T> void unique(T& c){c.erase(std::unique(c.begin(), c.end()), c.end());} template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;} template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;} template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;} template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << "(" << p.first << ", " << p.second << ")"; return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << "(" << itr->first << ", " << itr->second << ")"; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} // types using ll = long long int; using P = pair<int, int>; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1000000007; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // io struct fast_io{ fast_io(){ios_base::sync_with_stdio(false); cin.tie(nullptr); cout << fixed << setprecision(20);} } fast_io_; template<typename T> T extgcd(T a, T b, T &x, T &y){ T d = a; if(b != 0){ d = extgcd(b, a % b, y, x); y -= (a / b) * x; }else{ x = 1, y = 0; } return d; } template <typename T> T modinv(T a, T m){ long long x = 0, y = 0; extgcd<long long>(a, m, x, y); x %= m; if(x < 0)x += m; return x; } const int B = 2500; ll dp[5010][5010]; ll fac[10010], inv[10010]; void construct(){ fac[0] = 1; FOR(i, 1, 10001)fac[i] = fac[i-1] * i % mod; inv[10000] = modinv<ll>(fac[10000], mod); for(int i = 9999; i >= 0; i--){ inv[i] = inv[i+1] * (i+1) % mod; } } int main(int argc, char const* argv[]) { int n; cin >> n; vector<ll> a(n), b(n); rep(i, n)cin >> a[i] >> b[i]; construct(); rep(i, n){ dp[B-a[i]][B-b[i]]++; } rep(i, 5000){ rep(j, 5000){ if(i > 0)(dp[i][j] += dp[i-1][j]) %= mod; if(j > 0)(dp[i][j] += dp[i][j-1]) %= mod; } } ll res = 0; rep(i, n){ (res += dp[a[i]+B][b[i]+B]) %= mod; (res -= fac[2*a[i]+2*b[i]] * (inv[2*a[i]] * inv[2*b[i]] % mod) % mod) %= mod; } if(res < 0)res += mod; res = res * inv[2] % mod; cout << res << endl; return 0; }

codenet

s524177306

p04051

cpp

Accepted

#include <iostream> #include <sstream> #include <cstdio> #include <cstdlib> #include <cmath> #include <ctime> #include <cstring> #include <string> #include <vector> #include <stack> #include <queue> #include <deque> #include <map> #include <set> #include <bitset> #include <numeric> #include <utility> #include <iomanip> #include <algorithm> #include <functional> using namespace std; #define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl #define EACH(i, s) for (__typeof__((s).begin()) i = (s).begin(); i != (s).end(); ++i) template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; } template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; } template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P) { return s << '<' << P.first << ", " << P.second << '>'; } template<class T> ostream& operator << (ostream &s, vector<T> P) { for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; } template<class T> ostream& operator << (ostream &s, vector<vector<T> > P) { for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; } template<class T1, class T2> ostream& operator << (ostream &s, map<T1,T2> P) { EACH(it, P) { s << "<" << it->first << "->" << it->second << "> "; } return s << endl; } const int MAX = 500000; const int MOD = 1000000007; int N; int A[MAX], B[MAX]; inline long long mod(long long a, long long m) { return (a % m + m) % m; } struct Fp { long long val; Fp() : val(0) {} Fp(long long val_) { this->val = mod(val_, MOD); } Fp operator = (long long val_) { this->val = mod(val_, MOD); return *this; } inline Fp operator - () { return mod(-val, MOD); } inline const Fp& operator += (const Fp &x); inline const Fp& operator -= (const Fp &x); inline const Fp& operator *= (const Fp &x); inline const Fp& operator /= (const Fp &x); }; ostream &operator << (ostream &os, Fp x) { return os << x.val;} istream &operator >> (istream &is, Fp &x) { is >> x; return is; } bool operator == (Fp x, Fp y) { return mod(x.val, MOD) == mod(y.val, MOD); } inline Fp operator + (Fp x, Fp y) { return mod(x.val + y.val, MOD); } inline Fp operator - (Fp x, Fp y) { return mod(x.val - y.val, MOD); } inline Fp operator * (Fp x, Fp y) { return mod(x.val * y.val, MOD); } inline Fp operator / (Fp x, Fp y) { long long a = y.val, b = MOD, u = 1, v = 0; while (b) { long long t = a/b; a -= t*b; swap(a, b); u -= t*v; swap(u, v); } return x * u; } inline Fp power(Fp a, long long n) { if (n == 0) return Fp(1); Fp t = power(a, n/2); t = t * t; if (n & 1) t = t * a; return t; } inline const Fp& Fp::operator += (const Fp &x) {*this = *this + x; return *this;} inline const Fp& Fp::operator -= (const Fp &x) {*this = *this - x; return *this;} inline const Fp& Fp::operator *= (const Fp &x) {*this = *this * x; return *this;} inline const Fp& Fp::operator /= (const Fp &x) {*this = *this / x; return *this;} int Com[4010][4010]; void calc_com() { memset(Com, 0, sizeof(Com)); Com[0][0] = 1; for (int i = 1; i < 4010; ++i) { Com[i][0] = 1; Com[0][i] = 1; } for (int i = 1; i < 4010; ++i) { for (int j = 1; j < 4010; ++j) { Com[i][j] = (Com[i][j-1] + Com[i-1][j]); Com[i][j] %= MOD; } } } Fp dp[4010][4010]; long long solve() { Fp res = 0; memset(dp, 0, sizeof(dp)); for (int i = 0; i < N; ++i) { dp[2005-A[i]][2005-B[i]] += 1; } for (int i = 1; i < 4010; ++i) { for (int j = 1; j < 4010; ++j) { dp[i][j] += dp[i-1][j] + dp[i][j-1]; } } for (int i = 0; i < N; ++i) { res += dp[2005+A[i]][2005+B[i]]; } for (int i = 0; i < N; ++i) { res -= Com[A[i]*2][B[i]*2]; //cout << i << ": " <<Com[ A[i]*2 + B[i]*2 ][ A[i] * 2 ] << endl; } res /= 2; return res.val; } int main() { calc_com(); while (cin >> N) { for (int i = 0; i < N; ++i) cin >> A[i] >> B[i]; cout << solve() << endl; } }

codenet

s124887252

p04051

cpp

Accepted

#include <iostream> #define MOD 1000000007 #define MAX_N 200000 #define MAX_AB 2000 #define MAX_FACT 2 * ( 2 * MAX_AB + 1 ) using namespace std; namespace mod { template <uint_fast64_t mod> struct Modint { private: uint_fast64_t val; public: constexpr Modint( const uint_fast64_t val = 0 ) : val( val % mod ) {} constexpr uint_fast64_t &value() noexcept { return val; } constexpr const uint_fast64_t &value() const noexcept { return val; } constexpr Modint operator+( const Modint &rhs ) const noexcept { return Modint( *this ) += rhs; } constexpr Modint operator-( const Modint &rhs ) const noexcept { return Modint( *this ) -= rhs; } constexpr Modint operator*( const Modint &rhs ) const noexcept { return Modint( *this ) *= rhs; } constexpr Modint operator/( const Modint &rhs ) const noexcept { return Modint( *this ) /= rhs; } constexpr Modint &operator+=( const Modint &rhs ) noexcept { val += rhs.val; if ( val > mod ) val -= mod; return *this; } constexpr Modint &operator-=( const Modint &rhs ) noexcept { if ( val < rhs.val ) val += mod; val -= rhs.val; return *this; } constexpr Modint &operator*=( const Modint &rhs ) noexcept { val *= rhs.val; val %= mod; return *this; } constexpr Modint &operator/=( const Modint &rhs ) noexcept { uint_fast64_t a = rhs.val; uint_fast64_t b = mod; uint_fast64_t x = 1; uint_fast64_t y = 0; while ( b > 0 ) { uint_fast64_t q = a / b; a -= q * b; x -= q * y; swap( a, b ); swap( x, y ); } val *= ( x + mod ) % mod; val %= mod; return *this; } friend constexpr ostream &operator<<( ostream &o, const Modint &m ) { return ( o << ( m.val ) ); } friend constexpr istream &operator>>( istream &i, Modint &m ) { return ( i >> ( m.val ) ); } Modint pow( int n ) { Modint res = 1; Modint a = Modint( *this ); while ( n != 0 ) { if ( n & 1 ) res *= a; a *= a; n >>= 1; } return res; } }; // Modint Womparer template <uint_fast64_t mod> inline bool const operator<( const Modint<mod> &l, const Modint<mod> &r ) { return l.value() < r.value(); } template <uint_fast64_t mod> inline bool operator>( const Modint<mod> &l, const Modint<mod> &r ) { return r < l; } template <uint_fast64_t mod> inline bool operator<=( const Modint<mod> &l, const Modint<mod> &r ) { return !( l > r ); } template <uint_fast64_t mod> inline bool operator>=( const Modint<mod> &l, const Modint<mod> &r ) { return !( l < r ); } // Modint Equality Womparer template <uint_fast64_t mod> inline bool operator==( const Modint<mod> &l, const Modint<mod> &r ) { return l.value() == r.value(); } template <uint_fast64_t mod> inline bool operator!=( const Modint<mod> &l, const Modint<mod> &r ) { return !( l == r ); } } // namespace mod using mint_t = mod::Modint<MOD>; mint_t fact[MAX_FACT + 1]; void initFact() { fact[0] = 1; for ( int i = 0; i < MAX_FACT; i++ ) fact[i + 1] = fact[i] * ( i + 1 ); } mint_t comb( int n, int r ) { return fact[n] / fact[n - r] / fact[r]; } int A[MAX_N]; int B[MAX_N]; mint_t f[2 * MAX_AB + 1][2 * MAX_AB + 1]; int main( int argc, char **argv ) { initFact(); int N; cin >> N; for ( int i = 0; i < N; i++ ) cin >> A[i] >> B[i]; for ( int i = 0; i < N; i++ ) f[MAX_AB - A[i]][MAX_AB - B[i]] += 1; for ( int i = 0; i < 2 * MAX_AB + 1; i++ ) { for ( int j = 0; j < 2 * MAX_AB + 1; j++ ) { if ( i > 0 ) f[i][j] += f[i - 1][j]; if ( j > 0 ) f[i][j] += f[i][j - 1]; } } mint_t ans = 0; for ( int i = 0; i < N; i++ ) { ans += f[2000 + A[i]][2000 + B[i]]; ans -= comb( A[i] + A[i] + B[i] + B[i], A[i] + A[i] ); } ans /= 2; cout << ans << endl; return 0; }

codenet

s268343882

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define int long long #define stoi stoll using pii=pair<int,int>; #define all(c) begin(c),end(c) #define rall(c) rbegin(c),rend(c) #define fore(x,c) for(auto &&x:c) #define rep(i,a,n) for(int i=a,i##len=(int)(n);i<i##len;++i) #define rrep(i, a, n) for(int i=(int)(n-1);i>=a;--i) #define sz(c) ((int)c.size()) #define contains(c,x) (c.find(x)!=end(c)) #define inseg(l,x,r) ((l)<=(x)&&(x)<(r)) #define dump(...) #define pb push_back #define _ 0 const signed INF_=1001001001; const long long INF=1001001001001001001LL; const int DX[9]={0,1,0,-1,1,1,-1,-1,0},DY[9]={-1,0,1,0,-1,1,1,-1,0}; template<class T> ostream& operator<<(ostream &os,const vector<T> &v) { for (auto i = begin(v); i != end(v); i++) os<<*i<<(i==end(v)-1?"":" ");return os;} template<class T> istream& operator>>(istream &is,vector<T> &v) { for (auto i = begin(v); i != end(v); i++) is>>*i;return is;} template<class T,class U> istream& operator>>(istream &is, pair<T,U> &p) { is>>p.first>>p.second;return is;} template<class T, class U> bool chmax(T &a,const U &b){return a<b?a=b,1:0;} template<class T, class U> bool chmin(T &a,const U &b){return a>b?a=b,1:0;} template <class T> void psum(T& c) {partial_sum(begin(c), end(c), begin(c));} template<class T> using heap=priority_queue<T,vector<T>,greater<T>>; struct before_main_function { before_main_function() { cin.tie(0); ios::sync_with_stdio(0); cout << setprecision(15) << fixed; // #define endl "\n" } } before_main_function; //------------------8<------------------------------------8<-------------------- template <int mod> class ModInt { public: ModInt() : v(0) {} ModInt(int x) : v((x+mod)%mod) {} int value() const {return v;} const ModInt operator+(const ModInt &r) const { return ModInt(this->v + r.v); } const ModInt operator-(const ModInt &r) const { return ModInt(this->v + mod - r.v); } const ModInt operator*(const ModInt &r) const { return ModInt(this->v * r.v); } const ModInt operator/(const ModInt &r) const { return (*this * (~r)); } const ModInt operator^(int k) const { return ModInt(bpow(this->v, k)); } const ModInt operator~() const { return ModInt(bpow(this->v, mod-2)); } bool operator==(const ModInt &r) const { return this->v == r.v; } bool operator!=(const ModInt &r) const { return this->v != r.v; } ModInt& operator+=(const ModInt &r) { return *this = *this + r; } ModInt& operator-=(const ModInt &r) { return *this = *this - r; } ModInt& operator*=(const ModInt &r) { return *this = *this * r; } ModInt& operator/=(const ModInt &r) { return *this = *this * (~r); } private: int v; int bpow(int a, int b) const { int ret = 1; while (b > 0) { if (b & 1) ret = (ret * a) % mod; a = (a * a) % mod; b >>= 1; } return ret; } }; using Mint = ModInt<1000000007>; struct Factorial { static constexpr int MAX_N = 2000006; vector<Mint> fact, fact_inv; Factorial(size_t size = MAX_N) : fact(size), fact_inv(size) { fact[0] = fact_inv[0] = 1; for (int i = 1; i < MAX_N; ++i) { fact[i] = fact[i - 1] * i; fact_inv[i] = ~fact[i]; } } Mint combination(int N, int R) { if (N < R) return 0; return fact[N] * fact_inv[N - R] * fact_inv[R]; } static Mint bin_pow(Mint x, int p) { if (x.value() == 0) return x; Mint prod = 1; while (p > 0) { if (p & 1) prod *= x; x *= x; p >>= 1; } return prod; } }; signed main() { int N; cin >> N; vector<int> A(N), B(N); rep(i, 0, N) cin >> A[i] >> B[i]; vector<vector<Mint>> dp(4200, vector<Mint>(4200)); rep(i, 0, N) { dp[2100-A[i]][2100-B[i]] += 1; } rep(i, 0, 4190) { rep(j, 0, 4190) { dp[i + 1][j] += dp[i][j]; dp[i][j + 1] += dp[i][j]; } } Factorial fact; Mint ans = 0; rep(i, 0, N) { ans += dp[2100 + A[i]][2100 + B[i]]; ans -= fact.combination(2 * (A[i] + B[i]), 2 * B[i]); } ans /= 2; cout << ans.value() << endl; return (0^_^0); }

codenet

s930815663

p04051

cpp

Accepted

#pragma GCC optimize("Ofast") #include <bits/stdc++.h> #include <ext/pb_ds/assoc_container.hpp> #include <ext/pb_ds/tree_policy.hpp> using namespace std; using namespace __gnu_pbds; using ll = long long; using ull = unsigned long long; using pii = pair<int, int>; using pll = pair<long long, long long>; #define rep(i, n) for(int i = 0; i < (n); ++i) #define all(x) (x).begin(),(x).end() constexpr char ln = '\n'; constexpr long long MOD = 1000000007; //constexpr long long MOD = 998244353; template<class T1, class T2> inline bool chmax(T1 &a, T2 b) { if (a < b) { a = b; return true;} return false; } template<class T1, class T2> inline bool chmin(T1 &a, T2 b) { if (a > b) { a = b; return true;} return false; } inline int popcount(int x) {return __builtin_popcount(x);} inline int popcount(long long x) {return __builtin_popcountll(x);} void print() { cout << "\n"; } template<class T, class... Args> void print(const T &x, const Args &... args) { cout << x << " "; print(args...); } /////////////////////////////////////////////////////////////////////////////////////////////////////////////// template <uint_fast64_t Modulus> struct ModInt { using u64 = uint_fast64_t; u64 a; constexpr ModInt(const long long x = 0) noexcept : a(x >= 0 ? x % Modulus : (Modulus - (-x) % Modulus) % Modulus) {} constexpr u64 &value() noexcept {return a;} constexpr const u64 &value() const noexcept {return a;} constexpr ModInt operator+(const ModInt rhs) const noexcept {return ModInt(*this) += rhs;} constexpr ModInt operator-(const ModInt rhs) const noexcept {return ModInt(*this) -= rhs;} constexpr ModInt operator*(const ModInt rhs) const noexcept {return ModInt(*this) *= rhs;} constexpr ModInt operator/(const ModInt rhs) const noexcept {return ModInt(*this) /= rhs;} constexpr ModInt operator^(const long long rhs) const noexcept {return ModInt(*this) ^= rhs;} constexpr bool operator==(const ModInt &rhs) const noexcept {return a == rhs.a;} constexpr bool operator!=(const ModInt &rhs) const noexcept {return a != rhs.a;} constexpr ModInt &operator+=(const ModInt rhs) noexcept { a += rhs.a; if (a >= Modulus) { a -= Modulus; } return *this; } constexpr ModInt &operator-=(const ModInt rhs) noexcept { if (a < rhs.a) { a += Modulus; } a -= rhs.a; return *this; } constexpr ModInt &operator*=(const ModInt rhs) noexcept { a = a * rhs.a % Modulus; return *this; } constexpr ModInt &operator/=(ModInt rhs) noexcept { u64 exp = Modulus - 2; while (exp) { if (exp&1) *this *= rhs; exp >>= 1; rhs *= rhs; } return *this; } constexpr ModInt &operator^=(long long exp) noexcept { ModInt rhs = a; a = 1; while (exp) { if (exp&1) *this *= rhs; exp >>= 1; rhs *= rhs; } return *this; } friend ostream &operator<<(ostream& os, const ModInt& rhs) noexcept {return os << rhs.a;} friend istream &operator>>(istream& is, ModInt& rhs) noexcept {long long a; is >> a; rhs = a; return is;} }; using mint = ModInt<MOD>; struct ModCombination { vector<mint> Fac; vector<mint> Facinv; ModCombination(int x) { Fac.resize(x+1); Facinv.resize(x+1); Fac[0] = 1; for (int i = 0; i < x; ++i) Fac[i+1] = Fac[i]*(i+1); Facinv[x] = Fac[0]/Fac[x]; for (int i = x; i > 0; --i) Facinv[i-1] = Facinv[i]*i; } mint get(int n, int k) { if (k < 0 || k > n) return 0; return Fac[n]*Facinv[k]*Facinv[n-k]; } }; mint dp[4001][4001]; int main() { ios::sync_with_stdio(false); cin.tie(nullptr); int N; cin >> N; vector<int> A(N),B(N); rep(i,N) cin >> A[i] >> B[i]; rep(i,N) { dp[2000-A[i]][2000-B[i]] += 1; } rep(i,4001) { rep(j,4001) { if (i < 4000) dp[i+1][j] += dp[i][j]; if (j < 4000) dp[i][j+1] += dp[i][j]; } } mint ans = 0; rep(i,N) ans += dp[2000+A[i]][2000+B[i]]; ModCombination MC(8000); rep(i,N) ans -= MC.get(A[i]*2+B[i]*2,A[i]*2); ans /= 2; cout << ans << ln; }

codenet

s398157829

p04051

cpp

Accepted

#include <iostream> #include <vector> #include <map> #include <algorithm> using namespace std; #define COUT(x) cout << #x << " = " << (x) << " (L" << __LINE__ << ")" << endl template<class T1, class T2> ostream& operator << (ostream &s, pair<T1,T2> P) { return s << '<' << P.first << ", " << P.second << '>'; } template<class T> ostream& operator << (ostream &s, vector<T> P) { for (int i = 0; i < P.size(); ++i) { if (i > 0) { s << " "; } s << P[i]; } return s; } template<class T> ostream& operator << (ostream &s, vector<vector<T> > P) { for (int i = 0; i < P.size(); ++i) { s << endl << P[i]; } return s << endl; } template<int MOD> struct Fp { long long val; constexpr Fp(long long v = 0) noexcept : val(v % MOD) { if (val < 0) v += MOD; } constexpr int getmod() { return MOD; } constexpr Fp operator - () const noexcept { return val ? MOD - val : 0; } constexpr Fp operator + (const Fp& r) const noexcept { return Fp(*this) += r; } constexpr Fp operator - (const Fp& r) const noexcept { return Fp(*this) -= r; } constexpr Fp operator * (const Fp& r) const noexcept { return Fp(*this) *= r; } constexpr Fp operator / (const Fp& r) const noexcept { return Fp(*this) /= r; } constexpr Fp& operator += (const Fp& r) noexcept { val += r.val; if (val >= MOD) val -= MOD; return *this; } constexpr Fp& operator -= (const Fp& r) noexcept { val -= r.val; if (val < 0) val += MOD; return *this; } constexpr Fp& operator *= (const Fp& r) noexcept { val = val * r.val % MOD; return *this; } constexpr Fp& operator /= (const Fp& r) noexcept { long long a = r.val, b = MOD, u = 1, v = 0; while (b) { long long t = a / b; a -= t * b; swap(a, b); u -= t * v; swap(u, v); } val = val * u % MOD; if (val < 0) val += MOD; return *this; } constexpr bool operator == (const Fp& r) const noexcept { return this->val == r.val; } constexpr bool operator != (const Fp& r) const noexcept { return this->val != r.val; } friend constexpr ostream& operator << (ostream &os, const Fp<MOD>& x) noexcept { return os << x.val; } friend constexpr istream& operator >> (istream &is, Fp<MOD>& x) noexcept { return is >> x.val; } friend constexpr Fp<MOD> modpow(const Fp<MOD> &a, long long n) noexcept { if (n == 0) return 1; auto t = modpow(a, n / 2); t = t * t; if (n & 1) t = t * a; return t; } }; template<class T> struct BiCoef { vector<T> fact_, inv_, finv_; constexpr BiCoef(int n) noexcept : fact_(n, 1), inv_(n, 1), finv_(n, 1) { int MOD = fact_[0].getmod(); for(int i = 2; i < n; i++){ fact_[i] = fact_[i-1] * i; inv_[i] = -inv_[MOD%i] * (MOD/i); finv_[i] = finv_[i-1] * inv_[i]; } } constexpr T com(int n, int k) const noexcept { if (n < k || n < 0 || k < 0) return 0; return fact_[n] * finv_[k] * finv_[n-k]; } constexpr T fact(int n) const noexcept { if (n < 0) return 0; return fact_[n]; } constexpr T inv(int n) const noexcept { if (n < 0) return 0; return inv_[n]; } constexpr T finv(int n) const noexcept { if (n < 0) return 0; return finv_[n]; } }; const int MOD = 1000000007; using mint = Fp<MOD>; int main() { BiCoef<mint> bc(11000); int N; cin >> N; using pint = pair<int,int>; map<pint,int> ma; for (int i = 0; i < N; ++i) { int x, y; cin >> x >> y; ma[pint(x, y)]++; } const int GETA = 2500; vector<vector<mint> > dp(GETA*2, vector<mint>(GETA*2, 0)); for (auto it : ma) dp[GETA - it.first.first][GETA - it.first.second] = it.second; for (int i = 1; i < dp.size(); ++i) for (int j = 1; j < dp[0].size(); ++j) dp[i][j] += dp[i-1][j] + dp[i][j-1]; mint res = 0; for (auto it : ma) res += dp[it.first.first + GETA][it.first.second + GETA] * it.second; for (auto it : ma) res -= bc.com(it.first.first*2 + it.first.second*2, it.first.first*2) * it.second; cout << res * bc.inv(2) << endl; }

codenet

s598843101

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; using uint = unsigned int; using lint = long long int; using ulint = unsigned long long int; template<class T = int> using V = vector<T>; template<class T = int> using VV = V< V<T> >; template<class T, class U> void assign(V<T>& v, int n, const U& a) { v.assign(n, a); } template<class T, class... Args> void assign(V<T>& v, int n, const Args&... args) { v.resize(n); for (auto&& e : v) assign(e, args...); } template<class Int> constexpr bool is_prime(Int n) { if (n < 2 or n > 2 and ~n & 1) return false; for (Int i = 3; i * i <= n; i += 2) if (n % i == 0) return false; return true; } template<uint P> struct ModInt { static_assert(is_prime(P), "template argument must be a prime number"); using M = ModInt; uint v; ModInt() : v(0) {} template<class Int> ModInt(Int x) : v(x >= 0 ? x % P : -x % P ? P - -x % P : 0) {} constexpr ModInt(uint v, int _) : v(v) {} // 直接値を初期化 static constexpr uint p() { return P; } M operator++(int) { M t = *this; if (++v == P) v = 0; return t; } M operator--(int) { M t = *this; v = (v ? v : P) - 1; return t; } M& operator++() { if (++v == P) v = 0; return *this; } M& operator--() { v = (v ? v : P) - 1; return *this; } M operator+() const { return *this; } M operator-() const { return {v ? P - v : 0, 0}; } explicit operator bool() const noexcept { return v; } bool operator!() const noexcept { return !static_cast<bool>(*this); } M operator*(M rhs) const { return M(*this) *= rhs; } M operator/(M rhs) const { return M(*this) /= rhs; } M operator+(M rhs) const { return M(*this) += rhs; } M operator-(M rhs) const { return M(*this) -= rhs; } bool operator==(M rhs) { return v == rhs.v; } bool operator!=(M rhs) { return !(*this == rhs); } M& operator*=(M rhs) { v = (ulint) v * rhs.v % P; return *this; } M& operator/=(M rhs) { return *this *= rhs.inv(); } M& operator+=(M rhs) { v = rhs.v < P - v ? v + rhs.v : v - (P - rhs.v); return *this; } M& operator-=(M rhs) { v = rhs.v <= v ? v - rhs.v : v + (P - rhs.v); return *this; } M inv() const { assert(v); #ifdef __linux__ // ACとCFで動作を変えるための仮の対処 return pow(P - 2); #else int a = v, b = P, x = 1, u = 0; while (b) { int q = a / b; swap(a -= q * b, b); swap(x -= q * u, u); } return x; #endif } template<class Int> M pow(Int n) const { n = n >= 0 ? n % (P - 1) : P - 1 - -n % (P - 1); M res = 1; for (M a = *this; n > 0; a *= a, n >>= 1) if (n & 1) res *= a; return res; } template<class Int> friend M operator*(Int lhs, M rhs) { return M(lhs) *= rhs; } template<class Int> friend M operator/(Int lhs, M rhs) { return M(lhs) /= rhs; } template<class Int> friend M operator+(Int lhs, M rhs) { return M(lhs) += rhs; } template<class Int> friend M operator-(Int lhs, M rhs) { return M(lhs) -= rhs; } friend ostream& operator<<(ostream& os, M rhs) { return os << rhs.v; } friend istream& operator>>(istream& is, M& rhs) { lint x; is >> x; rhs = x; return is; } template<class Int> friend bool operator==(Int lhs, M rhs) { return M(lhs) == rhs; } template<class Int> friend bool operator!=(Int lhs, M rhs) { return !(lhs == rhs); } }; using Mint = ModInt<static_cast<uint>(1e9 + 7)>; V<Mint> fact, ifact; void init(int n) { assert(n >= 0); fact.resize(n + 1); fact[0] = 1; for (int i = 1; i <= n; ++i) { fact[i] = i * fact[i - 1]; } ifact.resize(n + 1); ifact[n] = fact[n].inv(); for (int i = n; i > 0; --i) { ifact[i - 1] = i * ifact[i]; } } Mint comb(int n, int r) { if (r < 0 or r > n) return 0; assert(n < (int) fact.size()); return fact[n] * ifact[r] * ifact[n - r]; } constexpr int N = 2000; int main() { cin.tie(nullptr); ios_base::sync_with_stdio(false); int n; cin >> n; V<> a(n), b(n); for (int i = 0; i < n; ++i) cin >> a[i] >> b[i]; VV<Mint> dp; assign(dp, 2 * N + 1, 2 * N + 1, 0); for (int i = 0; i < n; ++i) { ++dp[N - a[i]][N - b[i]]; } for (int x = 0; x <= 2 * N; ++x) for (int y = 0; y <= 2 * N; ++y) { if (x > 0) { dp[x][y] += dp[x - 1][y]; } if (y > 0) { dp[x][y] += dp[x][y - 1]; } } Mint res = 0; for (int i = 0; i < n; ++i) { res += dp[N + a[i]][N + b[i]]; } init(4 * N); for (int i = 0; i < n; ++i) { res -= comb(2 * (a[i] + b[i]), 2 * a[i]); } res /= 2; cout << res << '\n'; }

codenet

s058162660

p04051

cpp

Accepted

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; //template #define rep(i,a,b) for(int i=(a);i<(b);i++) #define rrep(i,a,b) for(int i=(a);i>(b);i--) #define ALL(v) (v).begin(),(v).end() typedef long long int ll; const int inf = 0x3fffffff; const ll INF = 0x1fffffffffffffff; const double eps=1e-12; string to_str(ll x){string res; while(x)res+=('0'+(x%10)),x/=10; reverse(ALL(res)); return res;} template<class T> inline bool chmax(T& a,T b){ if(a<b){a=b;return 1;}return 0; } template<class T> inline bool chmin(T& a,T b){ if(a>b){a=b;return 1;}return 0; } //template end template<unsigned mod>struct Mint { int val; int inv() const{ int tmp,a=val,b=mod,x=1,y=0; while(b)tmp=a/b,a-=tmp*b,swap(a,b),x-=tmp*y,swap(x,y); if(x<0)x+=mod; return x; } Mint():val(0){} Mint(ll x):val(x>=0?x%mod:mod+(x%mod)){} Mint pow(ll t){Mint res=1,b=*this; while(t){if(t&1)res*=b;b*=b;t>>=1;}return res;} Mint& operator+=(const Mint& x){if((val+=x.val)>=mod)val-=mod;return *this;} Mint& operator-=(const Mint& x){if((val+=mod-x.val)>=mod)val-=mod; return *this;} Mint& operator*=(const Mint& x){val=(ll)val*x.val%mod; return *this;} Mint& operator/=(const Mint& x){val=(ll)val*x.inv()%mod; return *this;} Mint operator+(const Mint& x)const{return Mint(*this)+=x;} Mint operator-(const Mint& x)const{return Mint(*this)-=x;} Mint operator*(const Mint& x)const{return Mint(*this)*=x;} Mint operator/(const Mint& x)const{return Mint(*this)/=x;} bool operator==(const Mint& x)const{return val==x.val;} bool operator!=(const Mint& x)const{return val!=x.val;} }; using mint=Mint<1000000007>; struct factorial { vector<mint> Fact, Finv; public: factorial(int maxx){ Fact.resize(maxx+1),Finv.resize(maxx+1); Fact[0]=mint(1); rep(i,0,maxx)Fact[i+1]=Fact[i]*(i+1); Finv[maxx]=mint(1)/Fact[maxx]; rrep(i,maxx,0)Finv[i-1]=Finv[i]*i; } mint fact(int n,bool inv=0){if(inv)return Finv[n];else return Fact[n];} mint nPr(int n,int r){if(n<0||n<r||r<0)return mint(0);else return Fact[n]*Finv[n-r];} mint nCr(int n,int r){if(n<0||n<r||r<0)return mint(0);else return Fact[n]*Finv[r]*Finv[n-r];} }; struct C{ float x,y; C(double _x=0,double _y=0):x(_x),y(_y){} C operator~()const{return {x,-y};} C operator+(const C& c)const{return {x+c.x,y+c.y};} C operator-(const C& c)const{return {x-c.x,y-c.y};} C operator*(const C& c)const{return {x*c.x-y*c.y,x*c.y+y*c.x};} }; vector<C> rt; void init(int lg=20){ rt.resize(1<<lg,1); rep(k,1,lg){ int d=1<<k; rep(i,0,d){ if(i&1)rt[d+i-1]=C(cos(2*M_PI*i/d),sin(2*M_PI*i/d)); else rt[d+i-1]=rt[(d+i)/2-1]; } } } void fft(vector<C>& a,bool inv=0,int n=-1){ if(n==-1)n=a.size(); if(inv){ for(int i=1;i<n;i<<=1){ for(int j=0;j<n;j+=i*2){ rep(k,0,i){ a[i+j+k]=a[i+j+k]*~rt[i*2-1+k]; const C tmp=a[j+k]-a[i+j+k]; a[j+k]=a[j+k]+a[i+j+k]; a[i+j+k]=tmp; } } } //rep(i,0,n)a[i].x/=n,a[i].y/=n; } else{ for(int i=n>>1;i;i>>=1){ for(int j=0;j<n;j+=i*2){ rep(k,0,i){ const C tmp=a[j+k]-a[i+j+k]; a[j+k]=a[j+k]+a[i+j+k]; a[i+j+k]=tmp*rt[i*2-1+k]; } } } } } //need to initialize int sz=1<<12; mint ans; factorial fact(8020); vector<vector<C>> buf(sz,vector<C>(sz)); void fft2d(bool inv=0){ rep(i,0,(inv?sz:sz/2))fft(buf[i],inv); rep(i,0,sz)rep(j,0,i)swap(buf[i][j],buf[j][i]); rep(i,0,sz)fft(buf[i],inv); if(inv)rep(i,0,sz)rep(j,0,sz)buf[i][j].x/=sz*sz; } map<pair<int,int>,int> mp; void sub(){ for(auto p1:mp)for(auto p2:mp){ int a=p1.first.first,b=p1.first.second; int c=p2.first.first,d=p2.first.second; ans+=fact.nCr(a+b+c+d,a+c)*p1.second*p2.second; } ans/=2; printf("%d\n",ans.val); exit(0); } int main(){ init(15); int n; scanf("%d",&n); rep(i,0,n){ int h,w; scanf("%d%d",&h,&w); mp[{h,w}]++; buf[h][w].x+=1.0; ans-=fact.nCr((h+w)*2,h*2); } if(mp.size()<=10000)sub(); fft2d(); rep(i,0,sz)rep(j,0,sz)buf[i][j]=buf[i][j]*buf[i][j]; fft2d(1); rep(i,0,sz)rep(j,0,sz){ mint tmp((ll)(buf[i][j].x+0.5)); ans+=fact.nCr(i+j,i)*tmp; } ans/=2; printf("%d\n",ans.val); return 0; }

codenet

s486366273

p04051

cpp

Accepted

/* Though leaves are many , the root is one. Through all the lying days of my youth I swayed my leaves and flowers in the sun. Now I may wither into the truth. - William Butler Yeats */ #pragma GCC optimize("Ofast,no-stack-protector") #pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx") //#pragma GCC target("avx,tune=native") #include<bits/stdc++.h> //#pragma comment("-Wl,--stack=1024000000") //#include<ext/pb_ds/assoc_container.hpp> using namespace std; namespace fastio{ char in[100000]; int itr=0,llen=0; char get(){ if(itr==llen)llen=fread(in,1,100000,stdin),itr=0; if(llen==0)return EOF; return in[itr++]; } char out[100000]; int itr2=0; void put(char c){ out[itr2++]=c; if(itr2==100000){ fwrite(out,1,100000,stdout); itr2=0; } } int clear(){ fwrite(out,1,itr2,stdout); itr2=0; return 0; } int getint(){ int ret=0;char ch=get(); if(ch=='-')return -getint(); while (ch<'0'||ch>'9'){ ch=get();if(ch=='-')return -getint(); } while ('0'<=ch&&ch<='9'){ ret=ret*10-48+ch; ch=get(); } return ret; } string getstr(){ string ret=""; char ch=get(); while(ch==' '||ch=='\n')ch=get(); while(ch!=' '&&ch!='\n')ret.push_back(ch),ch=get(); return ret; } void putstr(string s){ for(int i=0;i<s.size();i++)put(s[i]); } void putint(int x){ if(x<0){ put('-'); putint(-x); return; } if(x==0){ put('0');put(' '); return; } char c[40];int pos=0; while(x){ c[pos++]='0'+x%10; x/=10; } for(int i=pos-1;i>=0;i--)put(c[i]); put(' '); } void putln(int x){ if(x<0){ put('-'); putln(-x); return; } if(x==0){ put('0');put('\n'); return; } char c[40];int pos=0; while(x){ c[pos++]='0'+x%10; x/=10; } for(int i=pos-1;i>=0;i--)put(c[i]); put('\n'); } } using namespace fastio; //using namespace __gnu_pbds; const int inf=0x3f3f3f3f; const double eps=1e-6; const int mod=1000000007; typedef long long ll; #ifndef LOCAL #define cerr if(0)cout #define eprintf(...) 0 #else #define eprintf(...) fprintf(stderr, __VA_ARGS__) #endif inline string getstr(string &s,int l,int r){string ret="";for(int i=l;i<=r;i++)ret.push_back(s[i]);return ret;} int modpow(int x,int y,int md=mod){int ret=1;do{if(y&1)ret=(ll)ret*x%md;x=(ll)x*x%md;}while(y>>=1);return ret;} inline int Rand(){return rand()*32768+rand();} int n,a[200005],b[200005],s[200005]; int C[4005][4005],fact[8888],inv[8888],ind[200005],c[200005],d[200005],pos[4444]; ll sum[6666]; int comb(int nn,int mm){ return (ll)fact[nn]*inv[mm]%mod*inv[nn-mm]%mod; } bool cmp1(int x,int y){ return a[x]<a[y]; } int main(){ fact[0]=1; for(int i=1;i<8888;i++)fact[i]=(ll)fact[i-1]*i%mod; for(int i=0;i<8888;i++)inv[i]=modpow(fact[i],mod-2); n=getint(); // n=2e5; for(int i=1;i<=n;i++){ // a[i]=rand()%2000+1;b[i]=rand()%2000+1; a[i]=getint();b[i]=getint(); s[i]=a[i]+b[i]; } C[0][0]=1; for(int i=1;i<=4000;i++){ C[i][0]=C[i][i]=1; for(int j=1;j<i;j++){ C[i][j]=(C[i-1][j]+C[i-1][j-1])%mod; } } for(int i=1;i<=n;i++){ for(int j=-a[i];j<=b[i];j++){ sum[j+2222]+=C[s[i]][a[i]+j]; } } for(int j=-2000;j<=2000;j++){ sum[j+2222]%=mod; } /* for(int i=1;i<=n;i++)ind[i]=i; sort(ind+1,ind+n+1,cmp1); for(int i=1;i<=n;i++){ c[i]=a[ind[i]]; d[i]=b[ind[i]]; } memcpy(a,c,sizeof a); memcpy(b,d,sizeof b); int ans=0; memset(pos,inf,sizeof pos); for(int i=n;i>=1;i--){ pos[a[i]]=i; s[i]=a[i]+b[i]; } for(int i=2000;i>=0;i--)pos[i]=min(pos[i],pos[i+1]); for(int delta=-2000;delta<=0;delta++){ register ll val=0; for(int j=pos[-delta];j<=n;j++){ val+=C[s[j]][a[j]+delta]; } sum[delta+2222]=val%mod; } for(int delta=1;delta<=2000;delta++){ register ll val=0; for(int j=1;j<=n;j++){ val+=C[s[j]][a[j]+delta]; } sum[delta+2222]=val%mod; }*/ int ans=0; for(int i=-2000;i<=2000;i++){ ans+=(ll)sum[i+2222]*sum[-i+2222]%mod; ans%=mod; } for(int i=1;i<=n;i++){ ans-=comb(a[i]+a[i]+b[i]+b[i],a[i]+a[i]); if(ans<0)ans+=mod; } ans=((ll)ans*(mod+1)/2)%mod; cout<<ans<<endl; return 0; }

codenet

s833720085

p04051

cpp

Accepted

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; const int INF = 0x3f3f3f3f; const ll LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // const int MOD = 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; int mod = MOD; struct ModInt { unsigned val; ModInt(): val(0) {} ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {} ModInt pow(ll exponent) { ModInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; } ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; } ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; } ModInt &operator/=(const ModInt &x) { // assert(__gcd(static_cast<int>(x.val), mod) == 1); unsigned a = x.val, b = mod; int u = 1, v = 0; while (b) { unsigned tmp = a / b; swap(a -= tmp * b, b); swap(u -= tmp * v, v); } return *this *= u; } bool operator==(const ModInt &x) const { return val == x.val; } bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } bool operator<=(const ModInt &x) const { return val <= x.val; } bool operator>(const ModInt &x) const { return val > x.val; } bool operator>=(const ModInt &x) const { return val >= x.val; } ModInt &operator++() { if (++val == mod) val = 0; return *this; } ModInt operator++(int) { ModInt res = *this; ++*this; return res; } ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; } ModInt operator--(int) { ModInt res = *this; --*this; return res; } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt(val ? mod - val : 0); } ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; } friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; } }; ModInt abs(const ModInt &x) { return x; } struct Combinatorics { int val; // "val!" and "mod" must be disjoint. vector<ModInt> fact, fact_inv, inv; Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) { fact[0] = 1; FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i; fact_inv[val] = ModInt(1) / fact[val]; for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i]; } ModInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val && k <= val); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) { if (n < 0 || k < 0) return ModInt(0); return (k == 0 ? ModInt(1) : nCk(n + k - 1, k)); } }; int main() { const int M = 2000; Combinatorics com(M * 4); int n; cin >> n; vector<int> a(n), b(n); REP(i, n) cin >> a[i] >> b[i]; vector<vector<ModInt> > dp(M * 2 + 1, vector<ModInt>(M * 2 + 1, 0)); REP(i, n) ++dp[M - a[i]][M - b[i]]; REP(i, M * 2 + 1) REP(j, M * 2 + 1) { if (i + 1 <= M * 2) dp[i + 1][j] += dp[i][j]; if (j + 1 <= M * 2) dp[i][j + 1] += dp[i][j]; } ModInt ans = 0; REP(i, n) { ans += dp[M + a[i]][M + b[i]]; ans -= com.fact[a[i] * 2 + b[i] * 2] * com.fact_inv[a[i] * 2] * com.fact_inv[b[i] * 2]; } cout << ans / 2 << '\n'; return 0; }

codenet

s833720085

p04051

cpp

Accepted

#define _USE_MATH_DEFINES #include <bits/stdc++.h> using namespace std; #define FOR(i,m,n) for(int i=(m);i<(n);++i) #define REP(i,n) FOR(i,0,n) #define ALL(v) (v).begin(),(v).end() using ll = long long; const int INF = 0x3f3f3f3f; const ll LINF = 0x3f3f3f3f3f3f3f3fLL; const double EPS = 1e-8; const int MOD = 1000000007; // const int MOD = 998244353; const int dy[] = {1, 0, -1, 0}, dx[] = {0, -1, 0, 1}; const int dy8[] = {1, 1, 0, -1, -1, -1, 0, 1}, dx8[] = {0, -1, -1, -1, 0, 1, 1, 1}; template <typename T, typename U> inline bool chmax(T &a, U b) { return a < b ? (a = b, true) : false; } template <typename T, typename U> inline bool chmin(T &a, U b) { return a > b ? (a = b, true) : false; } struct IOSetup { IOSetup() { cin.tie(nullptr); ios_base::sync_with_stdio(false); cout << fixed << setprecision(20); } } iosetup; int mod = MOD; struct ModInt { unsigned val; ModInt(): val(0) {} ModInt(ll x) : val(x >= 0 ? x % mod : x % mod + mod) {} ModInt pow(ll exponent) { ModInt tmp = *this, res = 1; while (exponent > 0) { if (exponent & 1) res *= tmp; tmp *= tmp; exponent >>= 1; } return res; } ModInt &operator+=(const ModInt &x) { if((val += x.val) >= mod) val -= mod; return *this; } ModInt &operator-=(const ModInt &x) { if((val += mod - x.val) >= mod) val -= mod; return *this; } ModInt &operator*=(const ModInt &x) { val = static_cast<unsigned long long>(val) * x.val % mod; return *this; } ModInt &operator/=(const ModInt &x) { // assert(__gcd(static_cast<int>(x.val), mod) == 1); unsigned a = x.val, b = mod; int u = 1, v = 0; while (b) { unsigned tmp = a / b; swap(a -= tmp * b, b); swap(u -= tmp * v, v); } return *this *= u; } bool operator==(const ModInt &x) const { return val == x.val; } bool operator!=(const ModInt &x) const { return val != x.val; } bool operator<(const ModInt &x) const { return val < x.val; } bool operator<=(const ModInt &x) const { return val <= x.val; } bool operator>(const ModInt &x) const { return val > x.val; } bool operator>=(const ModInt &x) const { return val >= x.val; } ModInt &operator++() { if (++val == mod) val = 0; return *this; } ModInt operator++(int) { ModInt res = *this; ++*this; return res; } ModInt &operator--() { val = (val == 0 ? mod : val) - 1; return *this; } ModInt operator--(int) { ModInt res = *this; --*this; return res; } ModInt operator+() const { return *this; } ModInt operator-() const { return ModInt(val ? mod - val : 0); } ModInt operator+(const ModInt &x) const { return ModInt(*this) += x; } ModInt operator-(const ModInt &x) const { return ModInt(*this) -= x; } ModInt operator*(const ModInt &x) const { return ModInt(*this) *= x; } ModInt operator/(const ModInt &x) const { return ModInt(*this) /= x; } friend ostream &operator<<(ostream &os, const ModInt &x) { return os << x.val; } friend istream &operator>>(istream &is, ModInt &x) { ll val; is >> val; x = ModInt(val); return is; } }; ModInt abs(const ModInt &x) { return x; } struct Combinatorics { int val; // "val!" and "mod" must be disjoint. vector<ModInt> fact, fact_inv, inv; Combinatorics(int val = 10000000) : val(val), fact(val + 1), fact_inv(val + 1), inv(val + 1) { fact[0] = 1; FOR(i, 1, val + 1) fact[i] = fact[i - 1] * i; fact_inv[val] = ModInt(1) / fact[val]; for (int i = val; i > 0; --i) fact_inv[i - 1] = fact_inv[i] * i; FOR(i, 1, val + 1) inv[i] = fact[i - 1] * fact_inv[i]; } ModInt nCk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val && k <= val); return fact[n] * fact_inv[k] * fact_inv[n - k]; } ModInt nPk(int n, int k) { if (n < 0 || n < k || k < 0) return ModInt(0); // assert(n <= val); return fact[n] * fact_inv[n - k]; } ModInt nHk(int n, int k) { if (n < 0 || k < 0) return ModInt(0); return (k == 0 ? ModInt(1) : nCk(n + k - 1, k)); } }; int main() { const int M = 2000; Combinatorics com(M * 4); int n; cin >> n; vector<int> a(n), b(n); REP(i, n) cin >> a[i] >> b[i]; vector<vector<ModInt> > dp(M * 2 + 1, vector<ModInt>(M * 2 + 1, 0)); REP(i, n) ++dp[M - a[i]][M - b[i]]; REP(i, M * 2 + 1) REP(j, M * 2 + 1) { if (i + 1 <= M * 2) dp[i + 1][j] += dp[i][j]; if (j + 1 <= M * 2) dp[i][j + 1] += dp[i][j]; } ModInt ans = 0; REP(i, n) { ans += dp[M + a[i]][M + b[i]]; ans -= com.fact[a[i] * 2 + b[i] * 2] * com.fact_inv[a[i] * 2] * com.fact_inv[b[i] * 2]; } cout << ans / 2 << '\n'; return 0; }

codenet

s484938385

p04051

cpp

Accepted

#include <iostream> #include <algorithm> #include <utility> #include <vector> #include <numeric> #include <tuple> template <class T, class U> inline bool chmin(T &lhs, const U &rhs) { if (lhs > rhs) { lhs = rhs; return true; } return false; } template <class T, class U> inline bool chmax(T &lhs, const U &rhs) { if (lhs < rhs) { lhs = rhs; return true; } return false; } // [l, r) from l to r struct range { struct itr { int i; constexpr itr(int i_): i(i_) { } constexpr void operator ++ () { ++i; } constexpr int operator * () const { return i; } constexpr bool operator != (itr x) const { return i != x.i; } }; const itr l, r; constexpr range(int l_, int r_): l(l_), r(std::max(l_, r_)) { } constexpr itr begin() const { return l; } constexpr itr end() const { return r; } }; // [l, r) from r to l struct revrange { struct itr { int i; constexpr itr(int i_): i(i_) { } constexpr void operator ++ () { --i; } constexpr int operator * () const { return i; } constexpr bool operator != (itr x) const { return i != x.i; } }; const itr r, l; constexpr revrange(int l_, int r_): l(l_ - 1), r(std::max(l_, r_) - 1) { } constexpr itr begin() const { return r; } constexpr itr end() const { return l; } }; template <class T> class modulo_int { public: static constexpr int mod = T::value; static_assert(mod > 0, "mod must be positive"); private: long long value; constexpr void normalize() { value %= mod; if (value < 0) value += mod; } public: constexpr modulo_int(long long value_ = 0): value(value_) { normalize(); } constexpr modulo_int operator - () const { return modulo_int(mod - value); } constexpr modulo_int operator ~ () const { return power(mod - 2); } constexpr long long operator () () const { return value; } constexpr modulo_int operator + (const modulo_int &rhs) const { return modulo_int(*this) += rhs; } constexpr modulo_int &operator += (const modulo_int &rhs) { if ((value += rhs.value) >= mod) value -= mod; return (*this); } constexpr modulo_int operator - (const modulo_int &rhs) const { return modulo_int(*this) -= rhs; } constexpr modulo_int &operator -= (const modulo_int &rhs) { if ((value += mod - rhs.value) >= mod) value -= mod; return (*this); } constexpr modulo_int operator * (const modulo_int &rhs) const { return modulo_int(*this) *= rhs; } constexpr modulo_int &operator *= (const modulo_int &rhs) { (value *= rhs.value) %= mod; return (*this); } constexpr modulo_int operator / (const modulo_int &rhs) const { return modulo_int(*this) /= rhs; } constexpr modulo_int &operator /= (const modulo_int &rhs) { return (*this) *= ~rhs; } constexpr bool operator == (const modulo_int &rhs) const { return value == rhs(); } constexpr bool operator != (const modulo_int &rhs) const { return value != rhs(); } constexpr modulo_int power (unsigned long long pow) const { modulo_int result(1), mult(*this); while (pow > 0) { if (pow & 1) result *= mult; mult *= mult; pow >>= 1; } return result; } friend std::istream &operator >> (std::istream &stream, modulo_int &lhs) { stream >> lhs.value; lhs.normalize(); return stream; } friend std::ostream &operator << (std::ostream &stream, const modulo_int &rhs) { return stream << rhs.value; } }; template <class T> class factorials { public: using value_type = T; public: std::vector<value_type> fact, fact_inv; factorials(int size_ = 200000): fact(size_ + 1), fact_inv(size_ + 1) { fact[0] = 1; for (int i = 1; i <= size_; ++i) { fact[i] = fact[i - 1] * value_type(i); } fact_inv[size_] = ~fact[size_]; for (int i = size_; i > 0; --i) { fact_inv[i - 1] = fact_inv[i] * value_type(i); } } value_type operator () (int n, int r) const { return fact[n] * fact_inv[n - r] * fact_inv[r]; } }; using modint = modulo_int<std::integral_constant<int, 1000000007>>; constexpr int mx = 2005; modint dp[mx * 2][mx * 2]; factorials<modint> fact(mx * 4); int main() { int N; std::cin >> N; std::vector<int> A(N), B(N); for (int i: range(0, N)) { std::cin >> A[i] >> B[i]; dp[mx - A[i]][mx - B[i]] += 1; } for (int i: range(0, mx * 2)) { for (int j: range(0, mx * 2)) { if (i > 0) dp[i][j] += dp[i - 1][j]; if (j > 0) dp[i][j] += dp[i][j - 1]; } } modint ans; for (int i: range(0, N)) { ans += dp[mx + A[i]][mx + B[i]]; ans -= fact(A[i] * 2 + B[i] * 2, A[i] * 2); } std::cout << ans / 2 << '\n'; return 0; }

codenet

s490243036

p04051

cpp

Accepted

#include<bits/stdc++.h> using namespace std; typedef long long int ll; // template {{{ 0 // using {{{ 1 using ll = long long int; using pii = pair<int,int>; using pll = pair<ll,ll>; using vi = vector<int>; using vl = vector<ll>; using vii = vector<pii>; using vll = vector<pll>; // }}} 1 // definition {{{ 1 // scaning {{{ 2 #define Scd(x) scanf("%d", &x) #define Scd2(x,y) scanf("%d%d", &x, &y) #define Scd3(x,y,z) scanf("%d%d%d", &x, &y, &z) #define Scll(x) scanf("%lld", &x) #define Scll2(x,y) scanf("%lld%lld", &x, &y) #define Scll3(x,y,z) scanf("%lld%lld%lld", &x, &y, &z) #define Scc(c) scanf("%c", &c); #define Scs(s) scanf("%s", s); #define Scstr(s) scanf("%s", &s); // }}} 2 // constants {{{ 2 #define EPS (1e-7) #define INF (2e9) #define PI (acos(-1)) // }}} 2 // systems {{{ 2 #define Repe(x,y,z) for(ll x = z; x < y; x++) #define Rep(x,y) Repe(x,y,0) #define RRepe(x,y,z) for(ll x = y-z-1; x >= 0; x--) #define RRep(x,y) RRepe(x,y,0) // }}} 2 // output {{{ 2 #define YesNo(a) (a)?printf("Yes\n"):printf("No\n") #define YESNO(a) (a)?printf("YES\n"):printf("NO\n") // }}} 2 // }}} 1 // input {{{ 1 // }}} 1 // }}} 0 const long long int mod = 1000000007; // PowMod( base, index, modulo) return base ** index % modulo {{{ // PowMod = base ** index % mod ( natural numbers ) inline constexpr long long int PowMod( long long int base, long long int index, long long int modulo = mod ){ if( index == 0 ) return 1; // O( log(index) ) if( index % 2 ){ return base * PowMod(base, index - 1, modulo) % modulo; }else{ long long int Phalf = index / 2; long long int half = PowMod(base, Phalf, modulo); return half * half % modulo; } } // }}} // modint {{{ struct modint{ long long int a; inline constexpr modint( long long int x = 0 ) noexcept : a(x % mod) {} inline constexpr long long int &value() noexcept { return a; } inline constexpr const long long int &value() const noexcept { return a; } inline constexpr modint operator+(const modint rhs) const noexcept{ return modint(*this) += rhs; } inline constexpr modint operator+(const int rhs) const noexcept{ return modint(*this) += rhs; } inline constexpr modint operator+(const long long int rhs) const noexcept{ return modint(*this) += rhs; } inline constexpr modint operator-(const modint rhs) const noexcept{ return modint(*this) -= rhs; } inline constexpr modint operator-(const int rhs) const noexcept{ return modint(*this) -= rhs; } inline constexpr modint operator-(const long long int rhs) const noexcept{ return modint(*this) -= rhs; } inline constexpr modint operator*(const modint rhs) const noexcept{ return modint(*this) *= rhs; } inline constexpr modint operator*(const int rhs) const noexcept{ return modint(*this) *= rhs; } inline constexpr modint operator*(const long long int rhs) const noexcept{ return modint(*this) *= rhs; } inline constexpr modint operator/(const modint rhs) const noexcept{ return modint(*this) /= rhs; } inline constexpr modint operator/(const int rhs) const noexcept{ return modint(*this) /= rhs; } inline constexpr modint operator/(const long long int rhs) const noexcept{ return modint(*this) /= rhs; } inline constexpr modint operator+=(const modint rhs) noexcept{ a += rhs.a; if( a >= mod ) a -= mod; return *this; } inline constexpr modint operator-=(const modint rhs) noexcept{ a -= rhs.a; if( a < 0 ) a += mod; return *this; } inline constexpr modint operator*=(const modint rhs) noexcept{ a = a * rhs.a % mod ; return *this; } inline constexpr modint operator/=(const modint rhs) noexcept{ a = a * PowMod(rhs.a,mod-2) % mod; return *this; } }; // }}} unsigned long long int rnd(){ static unsigned long long int x = time(0); x = x ^ (x << 13); x = x ^ (x >> 7); return x = x ^ (x << 17); } #define D 4000 int main() { int N; Scd(N); vi A(N),C(N); int a,b; Rep(i,N){ Scd2(a,b); // a = (rnd())%2000+1; // b = (rnd())%2000+1; A[i] = a; C[i] = a+b; } vector<modint> f(D*2+1,1); Rep(i,D*2){ f[i+1] = f[i]*(i+1); } modint X=0,Y=0; // 答えは(X-Y)/2 // Yから求める Rep(i,N){ Y += f[C[i]*2] / f[C[i]*2-A[i]*2] / f[A[i]*2]; } vector<modint> ff(D*2+1); vector<vector<modint>> fc(D+1,vector<modint>(D+1)); Rep(i,N){ fc[C[i]][D-A[i]] += 1; } RRep(ci,D+1){ // *= (1+x); RRep(fi,D*2){ ff[fi+1] += ff[fi]; } // += Fc[ci] Rep(i,D+1){ ff[i] += fc[ci][i]; } } Rep(i,2*D+1){ X += ff[2*D-i]*ff[i]; } printf ("%lld\n", (X-Y)/2 ); return 0; }

codenet

s042112234

p04051

cpp

Accepted

#include<iostream> #include<iomanip> #include<map> #include<unordered_map> #include<set> #include<unordered_set> #include<vector> #include<array> #include<string> #include<stack> #include<queue> #include<algorithm> #include<cassert> #include<functional> #include<random> #include<complex> #include<bitset> #include<chrono> //#include<boost/multiprecision/cpp_int.hpp> #define int int64_t #define uint uint64_t #define REP(i, a, b) for (int64_t i = (int64_t)(a); i < (int64_t)(b); i++) #define rep(i, a) REP(i, 0, a) #define EACH(i, a) for (auto i: a) #define ITR(x, a) for (auto x = a.begin(); x != a.end(); x++) #define ALL(a) (a.begin()), (a.end()) #define HAS(a, x) (a.find(x) != a.end()) #define Min(x) *min_element(ALL(x)) #define Max(x) *max_element(ALL(x)) #define Unique(L) (L.erase(unique(ALL(L)), L.end())) #define veccat(v1, v2) std::copy((v2).begin(),(v2).end(),std::back_inserter(v1)/*v1の後ろにv2を入れる*/) #define intmax (std::numeric_limits<int64_t>::max() / 4) using namespace std; //typedef boost::multiprecision::cpp_int bigint; const double EPS = 1e-9; const double PI = acos(-1.0); class modint { //MODが素数であることを前提として実装してあるが、その判定はしていない。 //あまりが出るような除算をしてはいけない。 private: static const int MOD = 1000000007; public: modint() { //assert(is_prime(MOD)); this->number = 0; } modint(const int src) { //assert(is_prime(MOD)); this->number = opposit(src); } modint(const modint &src) { this->number = src.number; } modint& operator += (const modint& obj) { this->number = san2(this->number + obj.number); return *this; } modint& operator -= (const modint& obj) { this->number = san2(this->number - obj.number + MOD); return *this; } modint& operator *= (const modint& obj) { this->number = (this->number * obj.number) % MOD; return *this; } modint& operator /= (const modint& obj) { this->number = (this->number * inverse(obj.number)) % MOD; return *this; } modint& operator += (const int n) { this->number = san2(this->number + opposit(n)); return *this; } modint& operator -= (const int n) { this->number = san2(this->number - opposit(n) + MOD); return *this; } modint& operator *= (const int n) { this->number = (this->number * opposit(n)) % MOD; return *this; } modint& operator /= (const int n) { this->number = (this->number * inverse(n)) % MOD; return *this; } modint operator + (const modint obj) { modint re(*this); return re += obj; } modint operator - (const modint obj) { modint re(*this); return re -= obj; } modint operator * (const modint obj) { modint re(*this); return re *= obj; } modint operator / (const modint obj) { modint re(*this); return re /= obj; } modint operator + (const int n) { modint re(*this); return re += n; } modint operator - (const int n) { modint re(*this); return re -= n; } modint operator * (const int n) { modint re(*this); return re *= n; } modint operator / (const int n) { modint re(*this); return re /= n; } modint operator = (const int n) { this->number = opposit(n); return *this; } int get() { return number; } private: int number; int opposit(int n) { if (n < 0)n = MOD - ((-n) % MOD); return n % MOD; } int inverse(int n) { n = opposit(n); int result = 1; for (int i = MOD - 2; i; i /= 2) { if (i % 2)result = (result * n) % MOD; n = (n * n) % MOD; } return result; } inline int san2(const int n) { return MOD <= n ? n - MOD : n; } bool is_prime(int n) { if (n <= 1)return false; if (n == 2)return true; if (n % 2 == 0) return false; const int upperbound = int(sqrt(n)); for (int i = 3; i <= upperbound; i += 2) { if (n % i == 0) return false; } return true; } }; struct combi { public: vector<modint>facto; combi(const int N) :facto(N) { facto[0] = 1; REP(i, 1, N)facto[i] = facto[i - 1] * i; } modint get_combi(const int N, const int C) { //combination(N,C)を求めて返す。 assert(0 <= C && C <= N); if (int(facto.size()) <= N) { int a = facto.size(); facto.resize(N + 1); REP(i, a, N + 1)facto[i] = facto[i - 1] * i; } return facto[N] / (facto[N - C] * facto[C]); } }; signed main() { cin.tie(0); ios::sync_with_stdio(false); combi C(10000); int N; cin >> N; vector<int>A(N), B(N); rep(i, N)cin >> A[i] >> B[i]; modint X = 0;//解説のX vector<vector<modint>>grid(4011, vector<modint>(4011, 0)); vector<vector<int>>goal(4010, vector<int>(4010, 0)); rep(i, N) { grid[2005 - A[i]][2005 - B[i]] += 1; goal[2005 + A[i]][2005 + B[i]]++; } rep(i, 4010)rep(j, 4010) { if (goal[i][j])X += grid[i][j] * goal[i][j]; grid[i + 1][j] += grid[i][j]; grid[i][j + 1] += grid[i][j]; } modint X_ii = 0; rep(i, N) { X_ii += C.get_combi((A[i] + B[i]) * 2, B[i] * 2); } cout << ((X - X_ii) / 2).get() << endl; return 0; }

codenet

s488452186

p04051

cpp

Accepted

#include <bits/stdc++.h> #define BIT(n) (1LL << (n)) #define BITF(n, i) (((n) >> i) & 1) #define REP(i, n) for (int i = 0; i < n; i++) #define REPB(i, n) for (int i = 0; i < BIT(n); i++) #define REPS(i, x) for (int i = 1; i <= x; i++) #define REPR(i, n) for (int i = n; i >= 0; i--) #define REPZ(i, x) for (int i = 0; i <= x; i++) #define FOR(i, m, n) for (int i = m; i < n; i++) #define FORA(i, n) for (auto &&i : n) #define FORS(i, m, n) for (int i = m; i <= n; i++) using namespace std; #define PRINTARR(x, y) \ cerr << #x << "=\n"; \ for (auto itr = x; itr != y; itr++) cerr << *itr << " "; \ cerr << endl; #define PRINTARR2(x, i0, i1) \ cerr << #x << "=\n"; \ for (int ii0 = 0; ii0 < i0; ii0++) { \ for (int ii1 = 0; ii1 < i1; ii1++) cerr << x[ii0][ii1] << " "; \ cerr << endl; \ } #define DUMPOUT cerr // vector template <typename T> istream &operator>>(istream &is, vector<T> &vec) { for (T &x : vec) is >> x; return is; } // pair template <typename T, typename U> ostream &operator<<(ostream &os, pair<T, U> &pair_var) { os << "(" << pair_var.first << ", " << pair_var.second << ")"; return os; } // vector template <typename T> ostream &operator<<(ostream &os, const vector<T> &vec) { os << "{"; REP(i, (int)vec.size()) os << vec[i] << (i + 1 == (int)vec.size() ? "" : ", "); os << "}"; return os; } // map template <typename T, typename U> ostream &operator<<(ostream &os, map<T, U> &map_var) { os << "{"; FORA(itr, map_var) { os << *itr; itr++; if (itr != map_var.end()) os << ", "; itr--; } os << "}"; return os; } // set template <typename T> ostream &operator<<(ostream &os, set<T> &set_var) { os << "{"; FORA(itr, set_var) { os << *itr; itr++; if (itr != set_var.end()) os << ", "; itr--; } os << "}"; return os; } void dump_func() { DUMPOUT << endl; } template <class Head, class... Tail> void dump_func(Head &&head, Tail &&... tail) { DUMPOUT << head; if (sizeof...(Tail) > 0) DUMPOUT << ", "; dump_func(std::move(tail)...); } #ifdef DEBUG_ #define DEB #define DUMP(...) \ DUMPOUT << " " << string(#__VA_ARGS__) << ": " \ << "[" << to_string(__LINE__) << ":" << __FUNCTION__ << "]" << endl \ << " ", \ dump_func(__VA_ARGS__) #else #define DEB if (false) #define DUMP(...) #endif #define ALL(v) v.begin(), v.end() #define fst first #define snd second #define mp make_pair #define pb push_back #define epb emplace_back #define int long long #define pint pair<int, int> #define ld long double using namespace std; template <class T> bool chmax(T &a, const T &b) { if (a < b) { a = b; return 1; } return 0; } template <class T> bool chmin(T &a, const T &b) { if (a > b) { a = b; return 1; } return 0; } template <class T> using vec = std::vector<T>; template <class T> void print(const T &x) { cout << x << "\n"; } const int MOD = 1000000007, INF0 = 1061109567, INF = INF0 * INF0; const double EPS = 1e-10, PI = acos(-1.0); const int dx[4] = {1, 0, -1, 0}, dy[4] = {0, 1, 0, -1}; const int FACTSIZE = 10100; int fact[FACTSIZE]; int revfact[FACTSIZE]; int binpow(int a, int b, int mo) { int ans = 1; do { if (b & 1) ans = 1ll * ans * a % mo; a = 1ll * a * a % mo; } while (b >>= 1); return ans; } int ncr(int n, int r) { if (n < r) return 0; int rs = fact[n] * revfact[r]; if (rs >= MOD) rs %= MOD; rs *= revfact[n - r]; if (rs >= MOD) rs %= MOD; return rs; } void init() { fact[0] = 1, revfact[0] = 1; for (int i = 1; i < FACTSIZE; ++i) { fact[i] = fact[i - 1] * i % MOD; revfact[i] = binpow(fact[i], MOD - 2, MOD); } } #define MAXN 200200 //----// int N; int a[MAXN]; int b[MAXN]; int dp[4001][4001]; signed main() { init(); cin.tie(0), ios::sync_with_stdio(false); cout << fixed << setprecision(10); cin >> N; REP(i, N) cin >> a[i] >> b[i]; REP(i, N) { dp[2000 - a[i]][2000 - b[i]]++; } // REP(i, N) { dp[2000 + a[i]][2000 + b[i]]++; } REP(i, 4001) { REP(j, 4001) { // if (i > 0 && j > 0) dp[i][j] += dp[i - 1][j - 1]; if (i > 0) dp[i][j] += dp[i - 1][j]; if (j > 0) dp[i][j] += dp[i][j - 1]; dp[i][j] %= MOD; } } int ans = 0; REP(i, N) { ans += dp[2000 + a[i]][2000 + b[i]], ans %= MOD; } // DUMP(dp[1999][1999], dp[2000][2000], ans); int cnt = 0; REP(i, N) cnt += ncr(2 * (a[i] + b[i]), 2 * a[i]), cnt %= MOD; cnt = MOD - cnt; ans += cnt; ans %= MOD; ans = ans * revfact[2]; ans %= MOD; print(ans); }

codenet

s439259772

p04051

cpp

Accepted

#include <iostream> #include <vector> #include <cstdio> #include <sstream> #include <map> #include <string> #include <algorithm> #include <queue> #include <cmath> #include <functional> #include <set> #include <ctime> #include <random> #include <chrono> #include <cassert> #include <tuple> #include <utility> using namespace std; namespace { using Integer = long long; //__int128; template<class T, class S> istream& operator >> (istream& is, pair<T,S>& p){return is >> p.first >> p.second;} template<class T> istream& operator >> (istream& is, vector<T>& vec){for(T& val: vec) is >> val; return is;} template<class T> istream& operator , (istream& is, T& val){ return is >> val;} template<class T, class S> ostream& operator << (ostream& os, const pair<T,S>& p){return os << p.first << " " << p.second;} template<class T> ostream& operator << (ostream& os, const vector<T>& vec){for(size_t i=0; i<vec.size(); i++) os << vec[i] << (i==vec.size()-1?"":" "); return os;} template<class T> ostream& operator , (ostream& os, const T& val){ return os << " " << val;} template<class H> void print(const H& head){ cout << head; } template<class H, class ... T> void print(const H& head, const T& ... tail){ cout << head << " "; print(tail...); } template<class ... T> void println(const T& ... values){ print(values...); cout << endl; } template<class H> void eprint(const H& head){ cerr << head; } template<class H, class ... T> void eprint(const H& head, const T& ... tail){ cerr << head << " "; eprint(tail...); } template<class ... T> void eprintln(const T& ... values){ eprint(values...); cerr << endl; } class range{ Integer start_, end_, step_; public: struct range_iterator{ Integer val, step_; range_iterator(Integer v, Integer step) : val(v), step_(step) {} Integer operator * (){return val;} void operator ++ (){val += step_;} bool operator != (range_iterator& x){return step_ > 0 ? val < x.val : val > x.val;} }; range(Integer len) : start_(0), end_(len), step_(1) {} range(Integer start, Integer end) : start_(start), end_(end), step_(1) {} range(Integer start, Integer end, Integer step) : start_(start), end_(end), step_(step) {} range_iterator begin(){ return range_iterator(start_, step_); } range_iterator end(){ return range_iterator( end_, step_); } }; inline string operator "" _s (const char* str, size_t size){ return move(string(str)); } constexpr Integer my_pow(Integer x, Integer k, Integer z=1){return k==0 ? z : k==1 ? z*x : (k&1) ? my_pow(x*x,k>>1,z*x) : my_pow(x*x,k>>1,z);} constexpr Integer my_pow_mod(Integer x, Integer k, Integer M, Integer z=1){return k==0 ? z%M : k==1 ? z*x%M : (k&1) ? my_pow_mod(x*x%M,k>>1,M,z*x%M) : my_pow_mod(x*x%M,k>>1,M,z);} constexpr unsigned long long operator "" _ten (unsigned long long value){ return my_pow(10,value); } inline int k_bit(Integer x, int k){return (x>>k)&1;} //0-indexed mt19937 mt(chrono::duration_cast<chrono::nanoseconds>(chrono::steady_clock::now().time_since_epoch()).count()); template<class T> string join(const vector<T>& v, const string& sep){ stringstream ss; for(size_t i=0; i<v.size(); i++){ if(i>0) ss << sep; ss << v[i]; } return ss.str(); } inline string operator * (string s, int k){ string ret; while(k){ if(k&1) ret += s; s += s; k >>= 1; } return ret; } } constexpr long long mod = 9_ten + 7; class combination_mod{ const long long mod; const long long size; vector<long long> fact; //n! vector<long long> fact_inv; // (n!)^-1 void make_fact(){ fact[0] = 1; for(long long i=1; i<size; i++){ fact[i] = fact[i-1]*i % mod; } } void make_fact_inv(){ fact_inv[0] = fact_inv[1] = 1; for(long long i=2; i<size; i++){ fact_inv[i] = fact_inv[mod%i] * (mod - mod/i) % mod; // x ^ -1 } for(int i=2; i<size; i++){ fact_inv[i] = fact_inv[i-1] * fact_inv[i] % mod; // x! ^ -1 } } public: combination_mod(long long mod_, long long size_ = 2000000) : mod(mod_), size(size_+1){ fact.resize(size); fact_inv.resize(size); make_fact(); make_fact_inv(); } //nCk mod p O(1) long long operator()(long long n, long long k){ if(k==0 || n==k) return 1; long long ret = fact[n] * fact_inv[k] % mod * fact_inv[n-k] % mod; return ret; } }; int main(){ int n; cin >> n; vector<int> a(n), b(n); for(int i=0; i<n; i++){ cin >> a[i],b[i]; } vector<vector<long long>> dp(4010, vector<long long>(4010, 0)); int geta = 2005; for(int i=0; i<n; i++){ dp[ geta - a[i] ][ geta - b[i] ]++; } for(int i=0; i<4010; i++){ for(int j=0; j<4010; j++){ if(i) (dp[i][j] += dp[i-1][j]) %= mod; if(j) (dp[i][j] += dp[i][j-1]) %= mod; } } combination_mod cmb(mod, 200000); long long ans = 0; for(int i=0; i<n; i++){ ans += dp[ geta + a[i] ][ geta + b[i] ] - cmb(2*a[i]+2*b[i], 2*b[i]) + mod; ans %= mod; } ans = ans * my_pow_mod(2, mod-2, mod) % mod; println(ans); return 0; }

codenet

s086662812

p04051

cpp

Accepted

#include <bits/stdc++.h> using namespace std; #define LL long long #define LB long double #define ull unsigned long long #define x first #define y second #define pb push_back #define pf push_front #define mp make_pair #define Pair pair<int,int> #define pLL pair<LL,LL> #define pii pair<double,double> #define LOWBIT(x) x & (-x) // #define LOCAL true const int INF=2e9; const LL LINF=2e16; const int magic=348; const int MOD=1e9+7; const double eps=1e-10; const double pi=acos(-1); struct fastio { static const int S=1e7; char rbuf[S+48],wbuf[S+48];int rpos,wpos,len; fastio() {rpos=len=wpos=0;} inline char Getchar() { if (rpos==len) rpos=0,len=fread(rbuf,1,S,stdin); if (!len) return EOF; return rbuf[rpos++]; } template <class T> inline void Get(T &x) { char ch;bool f;T res; while (!isdigit(ch=Getchar()) && ch!='-') {} if (ch=='-') f=false,res=0; else f=true,res=ch-'0'; while (isdigit(ch=Getchar())) res=res*10+ch-'0'; x=(f?res:-res); } inline void getstring(char *s) { char ch; while ((ch=Getchar())<=32) {} for (;ch>32;ch=Getchar()) *s++=ch; *s='\0'; } inline void flush() {fwrite(wbuf,1,wpos,stdout);fflush(stdout);wpos=0;} inline void Writechar(char ch) { if (wpos==S) flush(); wbuf[wpos++]=ch; } template <class T> inline void Print(T x,char ch) { char s[20];int pt=0; if (x==0) s[++pt]='0'; else { if (x<0) Writechar('-'),x=-x; while (x) s[++pt]='0'+x%10,x/=10; } while (pt) Writechar(s[pt--]); Writechar(ch); } inline void printstring(char *s) { int pt=1; while (s[pt]!='\0') Writechar(s[pt++]); } }io; template<typename T> inline void check_max(T &x,T cmp) {x=max(x,cmp);} template<typename T> inline void check_min(T &x,T cmp) {x=min(x,cmp);} template<typename T> inline T myabs(T x) {return x>=0?x:-x;} template<typename T> inline T gcd(T x,T y) {return y==0?x:gcd(y,x%y);} inline int add(int x) {if (x>=MOD) x-=MOD;return x;} inline int add(int x,int MO) {if (x>=MO) x-=MO;return x;} inline int sub(int x) {if (x<0) x+=MOD;return x;} inline int sub(int x,int MO) {if (x<0) x+=MO;return x;} inline void Add(int &x,int y) {x=add(x+y);} inline void Add(int &x,int y,int MO) {x=add(x+y,MO);} inline void Sub(int &x,int y) {x=sub(x-y);} inline void Sub(int &x,int y,int MO) {x=sub(x-y,MO);} template<typename T> inline int quick_pow(int x,T y) {int res=1;while (y) {if (y&1) res=1ll*res*x%MOD;x=1ll*x*x%MOD;y>>=1;}return res;} template<typename T> inline int quick_pow(int x,T y,int MO) {int res=1;while (y) {if (y&1) res=1ll*res*x%MO;x=1ll*x*x%MO;y>>=1;}return res;} const int MAXN=2e5; int n; Pair a[MAXN+48]; Pair small[MAXN+48],big[MAXN+48];int stot,btot; const int lim=100000; int fac[lim+48],finv[lim+48]; inline void init_inv() { fac[0]=fac[1]=1; for (register int i=2;i<=lim;i++) fac[i]=1ll*fac[i-1]*i%MOD; finv[lim]=quick_pow(fac[lim],MOD-2); for (register int i=lim-1;i>=0;i--) finv[i]=1ll*finv[i+1]*(i+1)%MOD; } inline int C(int x,int y) { if (x<y || y<0) return 0; return 1ll*fac[x]*finv[y]%MOD*finv[x-y]%MOD; } int dp[5600][5600]; inline int calc_small() { int base=2748; for (register int i=1;i<=stot;i++) Add(dp[base-small[i].x][base-small[i].y],1); for (register int i=base-2748;i<=base+2748;i++) for (register int j=base-2748;j<=base+2748;j++) Add(dp[i+1][j],dp[i][j]),Add(dp[i][j+1],dp[i][j]); int ans=0; for (register int i=1;i<=stot;i++) Add(ans,dp[base+small[i].x][base+small[i].y]); for (register int i=1;i<=stot;i++) Sub(ans,C(small[i].x*2+small[i].y*2,small[i].x*2)); return ans; } /* inline int calc_big() { int ans=0; for (register int i=1;i<=btot-1;i++) for (register int j=i+1;j<=btot;j++) Add(ans,C(big[i].x+big[i].y+big[j].x+big[j].y,big[i].x+big[j].x)); return ans; } inline int calc_smallbig() { int ans=0,base=2748; for (register int i=1;i<=btot;i++) { for (register int j=base-2748;j<=base;j++) Add(ans,1ll*dp[base][j]*C(big[i].x-1+big[i].y-(j-base),big[i].x-1)); for (register int j=base;j>=base-2748;j--) Add(ans,1ll*dp[j][base]*C(big[i].x-(j-base)+big[i].y-1,big[i].x-(j-base))); } return ans; } */ int main () { double TIME=clock(); #ifdef LOCAL double TIME=clock(); freopen ("a.in","r",stdin); freopen ("a.out","w",stdout); cerr<<"Running..."<<endl; #endif // freopen ("gift.in","r",stdin); // freopen ("gift.out","w",stdout); io.Get(n); for (register int i=1;i<=n;i++) { io.Get(a[i].x),io.Get(a[i].y); if (a[i].x<=2700 && a[i].y<=2700) small[++stot]=a[i]; else big[++btot]=a[i]; } init_inv(); cout<<1ll*calc_small()*finv[2]%MOD<<endl; // io.Print(add(add(calc_small()+calc_big())+calc_smallbig()),'\n'); io.flush(); #ifdef LOCAL cerr<<"Exec Time: "<<(clock()-TIME)/CLOCKS_PER_SEC<<endl; #endif return 0; }

codenet

s386966305

p04051

cpp

Accepted

// includes #include <bits/stdc++.h> using namespace std; // macros #define pb emplace_back #define mk make_pair #define FOR(i, a, b) for(int i=(a);i<(b);++i) #define rep(i, n) FOR(i, 0, n) #define rrep(i, n) for(int i=((int)(n)-1);i>=0;i--) #define irep(itr, st) for(auto itr = (st).begin(); itr != (st).end(); ++itr) #define irrep(itr, st) for(auto itr = (st).rbegin(); itr != (st).rend(); ++itr) #define all(x) (x).begin(),(x).end() #define sz(x) ((int)(x).size()) #define UNIQUE(v) v.erase(unique(v.begin(), v.end()), v.end()) #define bit(n) (1LL<<(n)) // functions template <class T>bool chmax(T &a, const T &b){if(a < b){a = b; return 1;} return 0;} template <class T>bool chmin(T &a, const T &b){if(a > b){a = b; return 1;} return 0;} template <typename T> istream &operator>>(istream &is, vector<T> &vec){for(auto &v: vec)is >> v; return is;} template <typename T> ostream &operator<<(ostream &os, const vector<T>& vec){for(int i = 0; i < vec.size(); i++){ os << vec[i]; if(i + 1 != vec.size())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_set<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T> ostream &operator<<(ostream &os, const unordered_multiset<T>& st){for(auto itr = st.begin(); itr != st.end(); ++itr){ os << *itr; auto titr = itr; if(++titr != st.end())os << " ";} return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const pair<T1, T2> &p){os << p.first << " " << p.second; return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} template <typename T1, typename T2> ostream &operator<<(ostream &os, const unordered_map<T1, T2> &mp){for(auto itr = mp.begin(); itr != mp.end(); ++itr){ os << itr->first << ":" << itr->second; auto titr = itr; if(++titr != mp.end())os << " "; } return os;} // types using ll = long long int; using P = pair<int, int>; // constants const int inf = 1e9; const ll linf = 1LL << 50; const double EPS = 1e-10; const int mod = 1000000007; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, -1, 0, 1}; // io struct fast_io{ fast_io(){ios_base::sync_with_stdio(false); cin.tie(0); cout << fixed << setprecision(20);} } fast_io_; template <typename T> T power(T a, T n, T mod) { T res = 1; T tmp = n; T curr = a; while(tmp){ if(tmp % 2 == 1){ res = (T)(res * curr % mod); } curr = (T)(curr * curr % mod); tmp >>= 1; } return res; } struct Factorial{ int n = 0; static const long long mod_default = 1e9 + 7; long long MOD = mod_default; vector<long long> fac; vector<long long> inv_; explicit Factorial(){} explicit Factorial(int n, long long mod_=mod_default): n(n), MOD(mod_){ assert(MOD > 0 && n < MOD); fac.resize(n + 1); inv_.resize(n + 1); calc_factorial(); calc_inv(); } void calc_factorial(){ fac[0] = 1; for(int i = 1; i <= n; i++){ fac[i] = i * fac[i-1] % MOD; } } void calc_inv(){ inv_[n] = power<long long>(fac[n], MOD - 2, MOD); for(int i = n - 1; i >= 0; i--){ inv_[i] = (i + 1) * inv_[i+1] % MOD; } } long long& operator[](size_t i){ if((int)i > n){ cerr << "list index out of range" << endl; abort(); } return fac[i]; } long long inv(size_t i){ if((int)i > n){ cerr << "list index out of range" << endl; abort(); } return inv_[i]; } long long comb(int n, int k){ if(n < 0 || k < 0 || n < k)return 0; long long res = fac[n]; res = res * inv_[n-k] % MOD; res = res * inv_[k] % MOD; return res; } long long perm(int n, int k){ if(n < 0 || k < 0 || n < k)return 0; long long res = fac[n]; res = res * inv_[n-k] % MOD; return res; } long long h(int n, int k){ if(n == 0 && k == 0)return 1; return comb(n + k - 1, k); } }; ll dp[4010][4010]; const int B = 2000; int main(int argc, char const* argv[]) { int n; cin >> n; vector<ll> a(n), b(n); rep(i, n)cin >> a[i] >> b[i]; Factorial fac(5 * B); rep(i, n){ dp[B-a[i]][B-b[i]]++; } rep(i, 2 * B + 1){ rep(j, 2 * B + 1){ if(i > 0)(dp[i][j] += dp[i-1][j]) %= mod; if(j > 0)(dp[i][j] += dp[i][j-1]) %= mod; } } ll res = 0; rep(i, n){ res = (res + dp[B+a[i]][B+b[i]]) % mod; res = (res - fac.comb(2 * a[i] + 2 * b[i], 2 * a[i])) % mod; if(res < 0)res += mod; } res = res * fac.inv(2) % mod; cout << res << endl; return 0; }

codenet

s761371668

p04051

cpp

Accepted

/* Author: isaf27 (Ivan Safonov) */ #pragma GCC optimize("O3") #include <bits/stdc++.h> using namespace std; //defines typedef long long ll; typedef long double ld; #define TIME clock() * 1.0 / CLOCKS_PER_SEC #define fastIO ios_base::sync_with_stdio(0) #define nul point(0, 0) #define str_to_int(stroka) atoi(stroka.c_str()) #define str_to_ll(stroka) atoll(stroka.c_str()) #define str_to_double(stroka) atof(stroka.c_str()) #define what_is(x) cerr << #x << " is " << x << endl #define solve_system int number; cin >> number; for (int i = 0; i < number; i++) solve() #define solve_system_scanf int number; scanf("%d", &number); for (int i = 0; i < number; i++) solve() //permanent constants const ld pi = 3.141592653589793238462643383279; const ld log23 = 1.58496250072115618145373894394781; const ld eps = 1e-8; const ll INF = 1e18 + 239; const ll prost = 239; const int two = 2; const int th = 3; const ll MOD = 1e9 + 7; const ll MOD2 = MOD * MOD; const int BIG = 1e9 + 239; const int alf = 26; const int dx[4] = {-1, 0, 1, 0}; const int dy[4] = {0, 1, 0, -1}; const int dxo[8] = {-1, -1, -1, 0, 1, 1, 1, 0}; const int dyo[8] = {-1, 0, 1, 1, 1, 0, -1, -1}; const int dig = 10; const string str_alf = "abcdefghijklmnopqrstuvwxyz"; const string str_alf_big = "ABCDEFGHIJKLMNOPQRSTUVWXYZ"; const int day[12] = {31, 28, 31, 30, 31, 30, 31, 31, 30, 31, 30, 31}; const int digarr[10] = {6, 2, 5, 5, 4, 5, 6, 3, 7, 6}; const int bt = 31; const int fr = 4; //easy functions template< typename T > inline T gcd(T a, T b) { return a ? gcd(b % a, a) : b; } template< typename T > inline T lcm(T a, T b) { return (a / gcd(a, b)) * b; } inline bool is_down(char x) { return ('a' <= x && x <= 'z'); } inline bool is_upper(char x) { return ('A' <= x && x <= 'Z'); } inline bool is_digit(char x) { return ('0' <= x && x <= '9'); } ll power(ll a, int k) { if (k == 0) return 1; ll t = power(a, k >> 1); t = (t * t) % MOD; if (k & 1) t = (t * a) % MOD; return t; } //random mt19937 rnd(239); //constants const int M = 2 * 1e5 + 239; const int N = 2 * 1e3 + 239; const int L = 20; const int T = (1 << 20); const int B = trunc(sqrt(M)) + 1; const int X = 2010; const int X2 = 2 * X; const int MD = 1e9 + 7; int c[X2][X2], n, m, a[M], b[M], d[X][X]; ll f[X][X]; int main() { #ifdef ONPC freopen("input.txt", "r", stdin); freopen("output.txt", "w", stdout); #endif fastIO; cin >> n; for (int i = 0; i < n; i++) cin >> a[i] >> b[i]; m = 0; for (int i = 0; i < n; i++) { m = max(m, a[i]); m = max(m, b[i]); } for (int i = 0; i <= 2 * m; i++) { c[i][0] = 1; c[0][i] = 1; } for (int s = 2; s <= 4 * m; s++) for (int i = 1; i < min(2 * m + 1, s); i++) { int j = s - i; if (j <= 0 || j > 2 * m) continue; c[i][j] = c[i - 1][j] + c[i][j - 1]; if (c[i][j] >= MD) c[i][j] -= MD; } /*for (int i = 0; i <= 2 * m; i++, cerr << "\n") for (int j = 0; j <= 2 * m; j++, cerr << " ") cerr << c[i][j];*/ memset(d, 0, sizeof(d)); for (int i = 0; i < n; i++) d[a[i]][b[i]]++; for (int s = 2 * m; s >= 2; s--) for (int i = 1; i < min(s, m + 1); i++) { int j = s - i; if (j <= 0 || j > m) continue; d[i - 1][j] += d[i][j]; if (d[i - 1][j] >= MD) d[i - 1][j] -= MD; d[i][j - 1] += d[i][j]; if (d[i][j - 1] >= MD) d[i][j - 1] -= MD; d[i][j] = 0; } /*for (int i = 0; i <= m; i++, cerr << "\n") for (int j = 0; j <= m; j++, cerr << " ") cerr << d[i][j];*/ for (int j = 0; j <= m; j++) // (0, j) { f[0][j] = 0; for (int x = 0; x <= m; x++) // (x, 0) -- > (x + j, j) if (d[x][0] != 0) { f[0][j] += (ll)d[x][0] * (ll)c[x][j]; if (f[0][j] >= MOD2) f[0][j] -= MOD2; } for (int x = 1; x <= m; x++) // (0, x) -- > (x + j, 0) if (d[0][x] != 0) { f[0][j] += d[0][x]; if (f[0][j] >= MOD2) f[0][j] -= MOD2; } f[0][j] %= MOD; } for (int j = 0; j <= m; j++) // (j, 0) { f[j][0] = 0; for (int x = 0; x <= m; x++) // (x, 0) -- > (x + j, 0) if (d[x][0] != 0) { f[j][0] += d[x][0]; if (f[j][0] >= MOD2) f[j][0] -= MOD2; } for (int x = 1; x <= m; x++) // (0, x) -- > (x + j, x) if (d[0][x] != 0) { f[j][0] += (ll)d[0][x] * (ll)c[x][j]; if (f[j][0] >= MOD2) f[j][0] -= MOD2; } f[j][0] %= MOD; } for (int s = 2; s <= 2 * m; s++) for (int i = 1; i < min(m + 1, s); i++) { int j = s - i; if (j <= 0 || j > m) continue; f[i][j] = f[i - 1][j] + f[i][j - 1]; if (f[i][j] >= MD) f[i][j] -= MD; } ll ans = 0; for (int i = 0; i < n; i++) ans += f[a[i]][b[i]]; for (int i = 0; i < n; i++) ans -= c[2 * a[i]][2 * b[i]]; ans %= MOD; if (ans < 0) ans += MOD; if (ans & 1) ans = (ans + MOD) / 2; else ans /= 2; cout << ans; return 0; }

codenet