luogu 5505 [JSOI2011]分特产 广义容斥

Posted 2021-03-25 EM-LGH

code:

#include <bits/stdc++.h>   
#define N 10005   
#define LL long long 
using namespace std;  
const LL mod=1000000007;      
void setIO(string s) 
{
    string in=s+".in"; 
    string out=s+".out"; 
    freopen(in.c_str(),"r",stdin); 
} 
int a[N]; 
LL fac[N],inv[N],f[N],g[N];    
LL qpow(LL x,LL y) 
{
    LL tmp=1ll; 
    for(;y;y>>=1,x=x*x%mod) 
        if(y&1) tmp=tmp*x%mod;  
    return tmp;   
} 
LL Inv(LL x) { return qpow(x,mod-2); } 
LL C(int x,int y) 
{
    return fac[x]*inv[y]%mod*inv[x-y]%mod;       
}   
int main() 
{ 
    // setIO("input");  
    int i,j,n,m; 
    fac[0]=inv[0]=1ll; 
    for(i=1;i<N;++i) fac[i]=fac[i-1]*1ll*i%mod,inv[i]=Inv(fac[i]);         
    scanf("%d%d",&n,&m); 
    for(i=1;i<=m;++i) scanf("%d",&a[i]);        
    for(i=0;i<=n;++i) 
    {      
        f[i]=C(n,i);   
        for(j=1;j<=m;++j) (f[i]=f[i]*C(a[j]+n-i-1,n-i-1)%mod)%=mod;   
    }    
    for(i=0;i<=n;++i)  
    {
        (g[0]+=qpow(-1,i)*f[i]%mod+mod)%=mod;     
    } 
    printf("%lld
",g[0]);   
    return 0;     
}