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25/03/2023 00:17:13

# Рабочее место участника

## Задачи

1041. Pseudoprime numbers

Ограничения: время – 1s/2s, память – 64MiB Ввод: input.txt или стандартный ввод Вывод: output.txt или стандартный вывод
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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 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".

Sample Input

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


Output for Sample Input

no
no
yes
no
yes
yes

Source: Gordon V. Cormack, Waterloo local contest, 2007