1041. Pseudoprime numbers

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\ ≤\ 1\ 000\ 000\ 000` and `1\ <\ a\ <\ p`, determine whether or not `p` is a base-`a` pseudoprime.

Input contains several test cases followed by a line containing "0 0". Each test case consists of a line containing `p` and `a`. For each test case, output "yes" if p is a base-`a` pseudoprime; otherwise output "no".

3 2
10 3
341 2
341 3
1105 2
1105 3
0 0

no
no
yes
no
yes
yes