LTAI-22-01-16

#### Start

2022-01-11 04:00 AKST

## LTAI-22-01-16

#### End

2022-01-16 09:00 AKST
The end is near!
Contest is over.
Not yet started.
Contest is starting in -134 days 7:25:46

125:00:00

0:00:00

# Problem MPseudoprime 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