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

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.

For each input testcase, output one line:

• when there exists a solution, output three integers x, y and z, 1 ≤ x, y, z ≤ p-1. If there are multiple solutions, output any.
• when there's no solution, output one integer -1.

sample input	sample output
2 5 41 3 5	-1 1 2 4