POJ 3641 Pseudoprime numbers （伪素数_快速幂）

Description

Fermat's theorem states that for any prime number p and for any integer a > 1, a^p = a (mod p). That is, if we raise a to the p^th power and divide by p, the remainder is a. Some (but not very many) non-prime values of p, known as base-a pseudoprimes, have this property for some a. (And some, known as Carmichael Numbers, are base-a pseudoprimes for all a.)

Given 2 < p ≤ 1000000000 and 1 < a < p, determine whether or not p is a base-a pseudoprime.

Input

Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing p and a.

Output

For each test case, output "yes" if p is a base-a pseudoprime; otherwise output "no".

Sample Input

3 2
10 3
341 2
341 3
1105 2
1105 3
0 0

Sample Output

no
no
yes
no
yes
yes

#include<iostream>
#include<cstdio>
using namespace std;
typedef long long ll;
bool is_prime(int x)
{
	int i,j;
	for(i=2;i*i<=x;i++) if(x%i==0) return false;
	return true;
}

ll mod_pow(ll x,ll n,ll mod)
{
	ll res=1;
	while(n>0) {
		if(n&1) res=res*x%mod;
		x=x*x%mod;
		n>>=1;
	}
	return res;
}

int main()
{
	int a,p,i,j;
	while(cin>>p>>a) {
		if(p==0 && a==0) break;
		if(is_prime(p)) {
			printf("no\n");
			continue;
		}
		if(mod_pow(a,p,p)==a) printf("yes\n");
		else printf("no\n");
	}
	return 0;
}