Pseudoprime numbers(快速幂取模）

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<cstdio>
#include<cmath>
long long quickpow(long long a,long long p)
{
	 long long mod=p;
	long long ans=1,base=a;
	while(p)
	{
		if(p&1)
		{
			ans=(base*ans)%mod;
		}
		base=(base*base)%mod;
		p>>=1;
	}
	return ans;
}
long long su(int x)
{

	for(int i=2;i<=sqrt(x)+1;i++)
	{
		if(x%i==0)
		{
		       return 1;//不是素数输出1 
	    	}
	 } 
    return 0;
 } 
int main()
{
    long long a,p;
	while(~scanf("%lld%lld",&p,&a))
	{
		if(p==0&&a==0)
		break;
		if(quickpow(a,p)==a&&su(p)==1)
		printf("yes
");
		else
		printf("no
");
	}
	return 0;
}