511. Fermat's Last Theorem

Time limit per test: 0.75 second(s)
Memory limit: 262144 kilobytes
input: standard
output: standard

Given a positive integer n and a positive prime number p, find x, y and z such that x n+y n=z n modulo p and x, y and z are nonzero modulo p or report that there's no such triple.

Input
The first line of the input file contains the number t of testcases to solve, 1 ≤ t ≤ 1000. Each of the next t lines contains two integers n and p, 3 ≤ n ≤ 106, 2 ≤ p ≤ 106.

Output
For each input testcase, output one line:
  • when there exists a solution, output three integers x, y and z, 1 ≤ x, y, zp-1. If there are multiple solutions, output any.
  • when there's no solution, output one integer -1.


Example(s)
sample input
sample output
2
5 41
3 5
-1
1 2 4