xdoj-1149(多重集合+容斥原理+组合数取模）

#include <iostream>
#include <algorithm>
#include <cstdio>
using namespace std;
typedef long long LL;
const LL N=2e6;// 题目太坑了 提交 1e6会莫名错误 
const LL mod=1e9+7;
LL f[N+7];
LL inv_f[N+7];
LL n,m,k;
LL q_pow (LL x,LL k) {//快速幂求逆元
    LL ans=1;
    while (k) {
        if (k&1) ans=ans*x%mod;
        x=x*x%mod;
        k=(k>>1);
    }
    return ans%mod;
}
LL C (LL n, LL m) {// C(n,m)=n!/(m!*(n-m)!)
    if (n<m) return 0;
    LL t1=f[n];
    LL t2=inv_f[n-m]*inv_f[m]%mod;
    return t1*t2%mod;
}
int main ()
{
    f[0]=1;
    for (int i=1;i<=N;i++) 
        f[i]=f[i-1]*i%mod;// f[n]=n!
    inv_f[N]=q_pow(f[N],mod-2);
    for (int i=N-1;i>=0;i--)
        inv_f[i]=inv_f[i+1]*(i+1)%mod; // inv_f[i]=1/(n!); (逆元）
    while (cin>>n>>m>>k) {

        LL ans=C (m+n-1,n-1);// 组合数学多重集合挑选元素
        LL t=-1; LL num=m-(k+1);
        for (int i=1;num>=0&&i<=n;i++,t=-t,num-=(k+1)) {
                LL tmp=C(n,i)*C(num+n-1,n-1)%mod;// 容斥原理 
                ans=(ans+t*tmp+mod)%mod;
        }
        cout<<ans<<endl; 
    }
    return 0;
}