poj3641Pseudoprime numbers Time Limit: 1000MS Memory Limit: 65536K Total Submissions: 8854 Accepte

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Pseudoprime numbers

Time Limit: 1000MS		Memory Limit: 65536K
Total Submissions: 8854		Accepted: 3726

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

Sample Output

no
no
yes
no
yes
yes

Source

Waterloo Local Contest, 2007.9.23

#include<stdio.h>
#include<string.h>
__int64 powermod(__int64 a,__int64 b,__int64 c)
{
	__int64 ans=1;
	a=a%c;
	while(b)
	{
	   if(b%2)
	   ans=ans*a%c;
	   b/=2;
	   a=a*a%c;
	}
	return ans;
}
int judge(__int64 a)
{
	__int64 i;
	for(i=2;i*i<=a;i++)
	if(a%i==0)
	return 0;
	return 1;
}
int main()
{
	__int64 a,p,i,j;
	while(scanf("%I64d%I64d",&p,&a),p||a)
	{
		if(judge(p))
		printf("no\n");
		else
		{
		if(powermod(a,p,p)==a%p)
		printf("yes\n");
		else
		printf("no\n");
	    }
	}
	return 0;
}