Root

Input

The first line contains a single integer $t$ (1 \leq t \leq 10000) — the number of test cases. Each subsequent line contains integers $a$, $n$, and $p$ (1 \leq a, p \leq 10^6, 1 \leq n \leq 10, $p$ is prime, $a$ and $p$ are coprime).

Output

For each test, output all $n$-th degree roots of $a$ in the range $0$ to p-1 in ascending order on a single line, separated by a space. If there are no roots for the current test, print No root on a separate line.

Examples