Pseudoprime numbers

Time Limit: 1000 ms Memory Limit: 65536 KiB

Problem 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 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, have this property for some a. (And some, known as Carmichael Numbers, are base-a pseudoprimes for all a.)
Given 2 < p ≤ 1,000,000,000 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
341 2
0 0

Sample Output

no
yes

Hint

 

Source

HDU