P4700 算
背景
zhx和他的妹子出去玩。
描述
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" alt="" />
请在此填写题目描述
输入格式
仅一行,包含两个数N和M.
输出格式
仅一行,包含所求的答案mod 10^9 + 7的值。
【样例输入】
3 3
【样例输出】
56
备注
对于 50%的数据,所有1≤N,M≤1000。
对于100% 的数据,所有1≤N,M≤50000 。
题解:
等比数列:{a,aq1,aq2,aq3,aq4,aq5...aqn,...}
前m项的前缀和:s=a(1-qm)/(1-m);
费马小定理:若p为质数,ap-1%p=1
逆元:若ax%p=1(p为质数),则a,x互为逆元
则ans=sigma(1,n)q(1-qm)/(1-m)
由于同余定理不支持除法,逆元处理:
ans=sigma(1,n)q(1-qm)/(1-q)mod-2
考虑到负数问题
ans=sigma(1,n)q(qm-1)/(q-1)mod-2
最终
ans=sigma(1,n)q(qm-1)/(q-1)mod-2
代码:
#include<cstdio>
#include<iostream>
#define ll long long
using namespace std;
const ll mod=1e9+;
ll n,m;
inline ll fpow(ll a,ll p){
ll res=;
for(;p;p>>=,a=a*a%mod) if(p&) res=res*a%mod;
return res%mod;
}
inline void solve(){
ll ans=n;
for(ll i=,tmp,s;i<=n;i++){
/*自己推的*/
//tmp=fpow(i,m+1);
//s=((tmp-1+mod)%mod)*fpow(i-1,mod-2)%mod;
//ans=(ans+s-1+mod)%mod;
/*学哥讲的等比数列*/
tmp=i*(fpow(i,m)-)%mod;
s=fpow((i-),mod-);
ans=(ans+tmp*s%mod)%mod;
}//应该是都对
cout<<ans%mod;
}
int main(){
ios::sync_with_stdio(false);
cin>>n>>m;
solve();
return ;
}
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