【luoguP5091】【模板】欧拉定理

题目链接

欧拉定理：

当(a),(m)互质时，(a^{phi(m)}equiv 1 (mod ~ m))

扩展欧拉定理：

当(B>phi(m))时，(a^Bequiv a^{B~mod~phi(m)+phi(m)})

#include<iostream>
#include<cstring>
#include<cstdio>
#include<cmath>
#define int long long
using namespace std;

int a,m,b;
bool flag;

inline int read(int MOD){
	int x=0; char c=getchar();
	while(c<'0') c=getchar();
	while(c>='0'){
		x=x*10+c-'0';
		if(x>MOD) flag=1,x%=MOD;
		c=getchar();
	}
	return x;
}

inline int mul(int x,int y,int MOD){
	int s=0;
	while(y){
		if(y&1) s=(s+x)%MOD;
		y>>=1;
		x=(x+x)%MOD;
	}
	return s;
}

inline int qpow(int x,int k,int MOD){
	int s=1ll%MOD;
	while(k){
		if(k&1) s=mul(s,x,MOD);
		k>>=1;
		x=mul(x,x,MOD);
	}
	return s;
}

signed main()
{
	scanf("%lld%lld",&a,&m);
	int phi=m;
	int k=sqrt(m),x=m;
	for(int i=2;i<=k;++i)
		if(x%i==0){
			while(x%i==0) x/=i;
			phi=phi/i*(i-1);
		}
	if(x!=1) phi=phi/x*(x-1);
	b=read(phi);
	if(flag)
		printf("%lld
",qpow(a,b+phi,m));
	else printf("%lld
",qpow(a,b,m));
	return 0;
}