POJ 3641 pseudoprime numbers (pseudo prime number _ fast power)

Description

Fermat ' s theorem states, the for any prime number p and for any integer a > 1, ap = A (mod p). That's, if we raise a to the pth power and divide by P, the remainder is a. Some (but not very many) non-prime values of p, known as Base-a Pseudoprimes, has this property for Some a. (and Some, kn Own as Carmichael Numbers, is 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, the output "yes" if P is a base-a pseudoprime; Otherwise output "no".

Sample Input

3 2
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;
}