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Problem B: Count LCM

 

LCM is an abbreviation used for Least Common Multiple in Mathematics. We say LCM (a, b) = L if and only if L is the least integer which is divisible by both a and b.

You will be given N, M. You have to count number of pair (i, j) such that LCM (i, j) = i × j, where   1≤i≤N and 1≤j≤M.

 

Input

Input starts with an integer T (≤ 1000), denoting the number of test cases.

Each case starts with a line containing two integers N, M (1 ≤ N, M ≤ 109, and minimum of (N, M)106).

 

Output

For each case, print number of such pair.

 

Sample Input

Output for Sample Input

3

1 2

4 2

3 5

2

6

12

 

 

Problem Setter: Mohammad Hafiz Uddin

Alternate Solution: F. A. Rezaur Rahman Chowdhury