2018 ACM-ICPC 青岛站 L ZOJ 4069 容斥+枚举+组合计数

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//https://paste.ubuntu.com/p/727RRrKPn7/
#include<bits/stdc++.h>
using namespace std;
typedef long long ll;
const int maxn=1e5+5;
const ll mod=1e9+7;
ll fact[maxn],fact_inv[maxn],pow_2_inv[maxn],inv[maxn],ans;
void init()
{
    fact[0]=fact[1]=fact_inv[0]=fact_inv[1]=inv[0]=inv[1]=pow_2_inv[0]=1;;
    for(int i=2;i<maxn;i++)
    {
        inv[i]=(mod-mod/i)*inv[mod%i]%mod;
        fact[i]=fact[i-1]*i%mod;
        fact_inv[i]=fact_inv[i-1]*inv[i]%mod;
    }
    for(int i=1;i<maxn;i++)
        pow_2_inv[i]=pow_2_inv[i-1]*inv[2]%mod;
}
int main()
{
    init();
    int t,n,m;
    scanf("%d",&t);
    while(t--&&scanf("%d%d",&n,&m)!=EOF)
    {
        if(m>n)
            printf("0\n");
        else if(m==n)
            printf("%lld\n",fact[n-1]*inv[2]%mod);
        else
        {
            ans=0;
            for(int i=min(n-m,m);i>=0;--i)
                ans=(ans+(i&1?mod-1:1)*fact[n-m]%mod*fact_inv[n-m-i]%mod*fact_inv[i]%mod*fact[n-1-i]%mod*fact_inv[n-m-1]%mod*fact_inv[m-i]%mod*pow_2_inv[i]%mod)%mod;
            printf("%lld\n",ans*fact[n]%mod*fact_inv[n-m]%mod);
        }
    }
    return 0;
}