SP27942 PROD1GCD - Product it again

The problem is very simple. given two integers n and m, find the product GCD(1, 1) \* GCD(1, 2) \* ... \* GCD(1, M) \* GCD(2, 1) \* GCD(2, 2) \* ... \* GCD(2, M) \* ... \* GCD(N, 1) \* GCD(N, 2) \* ... \* GCD(N, M).

The first line will be the number of test cases t, followed by t lines , each having two numbers n and m (1

Output the required solution modulo 10^9+7.