BZOJ 2839: 集合计数 广义容斥

code: 

#include <bits/stdc++.h>   
#define N 1000005   
#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],poww[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,k; 
    fac[0]=inv[0]=poww[0]=1ll;           
    scanf("%d%d",&n,&k); 
    for(i=1;i<=n;++i) fac[i]=fac[i-1]*1ll*i%mod,inv[i]=Inv(fac[i]),poww[i]=poww[i-1]*2ll%(mod-1);
    for(i=0;i<=n;++i) f[i]=C(n,i)*qpow(2,poww[n-i])%mod;    
    LL ans=0ll;  
    for(i=k;i<=n;++i) (ans+=(qpow(-1,i-k)*C(i,k)%mod*f[i]%mod+mod)%mod)%=mod;  
    printf("%lld\n",ans); 
    return 0;     
}