Ivan the Terrible

Given three integer numbers $n$ , $a$ and $b$ , does there exist a natural $t$ such that $a^t \equiv b \bmod n$ ?

Input

Input consists of the number of cases $c$ , followed by $c$ triples with $n$ , $a$ and $b$ . You can assume $2 \le n \le 10^9$ , $0 \le a < n$ , and $0 \le b < n$ . Additionally, assume $c \le 200$ for the “hard private test cases”.

Output

For each case, print “YES” or “NO” depending on whether $a^t \equiv b \bmod n$ has at least one solution $t \ge 0$ or not.

Problem information

Author: Ivan Geffner

Generation: 2026-01-25T10:31:11.350Z