# Problem E

Pseudoprime numbers

Fermat’s theorem states that for any prime number
$p$ and for any integer
$a \ge 0$, $a^ p \equiv a \pmod{p}$. 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 $2 < p \le 1\, 000\,
000\, 000$ 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 1 | Sample Output 1 |
---|---|

3 2 10 3 341 2 341 3 1105 2 1105 3 0 0 |
no no yes no yes yes |