SP12721 PELL2 - Pell (Mid pelling)

D is a given positive integer, consider the equation : X² = D×Y² + 1, with X and Y positive integers. Find the minimum numbers (X,Y) within all solutions. Sometimes it's possible, sometimes not! Examples : If D=2, 3² = 2×2² + 1, so X=3 and Y=2. If D=3, 2² = 3×1² + 1, so X=2 and Y=1. If D=4, it's impossible!

The input begins with the number T of test cases in a single line. In each of the next T lines there is one integer D.

For each test case, if possible print X and Y the answer of the problem for D, else "-1".

T