P5091 模板欧拉定理

Posted 2021-02-10 lizehon

[题目链接] https://www.luogu.org/problemnew/show/P5091

(a^b mod m)

(1≤a≤10^9)
(1≤b≤10^{20000000})
(1≤m≤10^6)

U55950 【模板】扩展欧拉定理

// luogu-judger-enable-o2
#include<bits/stdc++.h>
#include<tr1/unordered_map>
using namespace std;
typedef long long LL;
const int INF=1e9+7;
inline LL read(){
    register LL x=0,f=1;register char c=getchar();
    while(c<48||c>57){if(c==‘-‘)f=-1;c=getchar();}
    while(c>=48&&c<=57)x=(x<<3)+(x<<1)+(c&15),c=getchar();
    return f*x;
}
inline LL read_mod(LL p){
    register LL x=0;register char c=getchar();
    while(c<48||c>57)c=getchar();
    while(c>=48&&c<=57)x=((x<<3)+(x<<1)+(c&15))%p,c=getchar();
    if(x==0) x=p;
    return x;
}

inline LL phi(LL n){
    LL res=n;
    for(LL i=2;i*i<=n;i++){
        if(n%i==0){
            res=res/i*(i-1);
            while(n%i==0) n/=i;
        }
    }
    if(n>1) res=res/n*(n-1);
    return res;
}

inline LL qpow(LL a,LL b,LL p){
    LL res=1;
    while(b){
        if(b&1) (res*=a)%=p;
        (a*=a)%=p;
        b>>=1;
    }
    return res;
}

LL a,mod,p,b;

int main(){
    a=read(),mod=read();
    a%=mod;
    p=phi(mod);
    b=read_mod(p);
    printf("%lld
",qpow(a,b,mod));
}