p5437 【XR-2】约定

分析

https://www.cnblogs.com/cjyyb/p/11111404.html

代码

#include<bits/stdc++.h>
using namespace std;
#define int long long
const int N = 1e7;
const int mod = ;
int fac[N+],inv[N+],pre[N+],y[N+],K,ik[N+],Ans,sur[N+];
inline int pw(int x,int p){
    int res=;
    while(p){
      if(p&)res=res*x%mod;
      x=x*x%mod;p>>=;
    }
    return res;
}
inline int work(){
    int i,j,k,res=,wh=((K+)&)?mod-:;
    for(i=;i<=K;i++,wh=mod-wh){
      int t=y[i];t=t*wh%mod;
      t=t*inv[i-]%mod*inv[K-i]%mod;
      t=t*pre[i-]%mod*sur[i+]%mod;
      res=(res+t+mod)%mod;
    }
    return res;
}
signed main(){
    int i,j,k,n;
    scanf("%lld%lld",&n,&K);
    K+=;fac[]=pre[]=sur[K+]=;
    for(i=;i<=K;i++)fac[i]=fac[i-]*i%mod;
    inv[K]=pw(fac[K],mod-);
    for(i=K-;i>=;i--)inv[i]=inv[i+]*(i+)%mod;
    for(i=;i<=K;i++)ik[i]=pw(i,K-);
    for(i=;i<=K;i++)pre[i]=pre[i-]*(n-i+mod)%mod;
    for(i=K;i>=;i--)sur[i]=sur[i+]*(n-i+mod)%mod;
    for(i=;i<=K;i++)y[i]=(y[i-]+(i-)*ik[i]%mod)%mod;
    Ans=(Ans+work())%mod;
    for(i=;i<=K;i++)y[i]=(y[i-]+ik[]*ik[i]%mod)%mod;
    Ans=(Ans+mod-work())%mod;
    for(i=;i<=K;i++)y[i]=(y[i-]+(n+n-i+)%mod*ik[i]%mod)%mod;
    Ans=(Ans+mod-work())%mod;
    for(i=;i<=K;i++)pre[i]=pre[i-]*(n+n-i+mod)%mod;
    for(i=K;i>=;i--)sur[i]=sur[i+]*(n+n-i+mod)%mod;
    Ans=(Ans+work())%mod;
    Ans=Ans*pw(n,mod-)%mod;printf("%lld\n",(Ans+mod)%mod);
    return ;
}