HeHe

In the equation X^2≡X(mod N) where x∈[0,N-1], we define He[N] as the number of solutions.
And furthermore, define HeHe[N]=He[1]*……*He[N]
Now here is the problem, write a program, output HeHe[N] modulo M for a given pair N, M.

First line: an integer t, representing t test cases.
Each test case contains two numbers N (1<=N<=10^7) and M (0<M<=10^9) separated by a space.

For each test case, output one line, including one integer: HeHe[N] mod m.

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2009 Multi-University Training Contest 8 - Host by BJNU