Pseudoprime numbers

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

不是素数，但满足a^p = a (mod p)，即a^p %p=a,为伪素数，输出 yes，否则输出no.

#include<stdio.h>      

__int64 ispri(__int64 num)  
{  
    for(int i=2;i*i<num;i++)  
    if(num%i==0)  
        return 0;  
    return 1;  
}  
__int64 quickpow(__int64 a,__int64 b,__int64 c)
{
__int64 tmp=a,res=1;
while(b)
{
if(b&1)
{
res*=tmp;
        res%=c;
        }
        tmp*=tmp;
        tmp%=c;
        b>>=1;
}
return res;   
}
int main()  
{  
    __int64 p,a;  
    while(~scanf("%I64d %I64d",&p,&a)&&(p||a))  
    {
 
    if(!ispri(p)&&quickpow(a,p,p)==a%p)  
        printf("yes\n");  
    else  
        printf("no\n");  
    }  
    return 0;  
}