Today Oz has an interesting problem for you. Oz has a set of M balls numbered from 0 to M-1. He has removed X balls from the set and calculated the sum of the numbers of removed balls. He has given you a hint that the sum is divisible by M.
Now your task is to count the number of ways of removing X balls. Output the answer modulo 10⁹+7.

Input:
First line contains one integer T - number of test cases.
Each test case contains two space separated integers M and X.

Output:
For each test case output the desired answer modulo 10⁹+7.

Constraints:
1 ≤ T ≤ 10
1 ≤ M ≤ 10⁹
1 ≤ X ≤ 10⁵
X ≤ M