Pseudoprime

Fermat's little theorem states the following.

If $p$ is prime, then for any integer $a > 1$ the congruence $a^p \equiv a \pmod{p}$ holds. In other words, raising $a$ to the $p$-th power and taking the remainder modulo $p$ gives back $a$.

However, even when $p$ is not prime, the congruence above may still hold for some integer $a$. In that case $p$ is called a pseudoprime to base $a$. (A composite number that satisfies the congruence for every $a$ is called a Carmichael number.)

Given $p$ and $a$, write a program that determines whether $p$ is a pseudoprime to base $a$.

The input consists of several test cases. Each test case is a single line containing two integers $p$ and $a$ separated by a space. The last line contains 0 0, which must not be processed.

$2 < p \le 10^9$, $1 < a < p$

For each test case, print yes if $p$ is a pseudoprime to base $a$, and no otherwise, one per line.