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D. Fun
time limit per test
2 seconds
memory limit per test
256 megabytes
input
standard input
output
standard output
Counting is Fun!
— satyam343

Given two integers n and x, find the number of triplets (a,b,c) of positive integers such that ab+ac+bcn and a+b+cx.

Note that order matters (e.g. (1,1,2) and (1,2,1) are treated as different) and a, b, c must be strictly greater than 0.

Input

The first line contains a single integer t (1t104)  — the number of test cases.

Each test case contains two integers n and x (1n,x106).

It is guaranteed that the sum of n over all test cases does not exceed 106 and that the sum of x over all test cases does not exceed 106.

Output

Output a single integer — the number of triplets (a,b,c) of positive integers such that ab+ac+bcn and a+b+cx.

Example
Input
4
7 4
10 5
7 1000
900000 400000
Output
4
10
7
1768016938
Note

In the first test case, the triplets are (1,1,1), (1,1,2), (1,2,1), and (2,1,1).

In the second test case, the triplets are (1,1,1), (1,1,2), (1,1,3), (1,2,1), (1,2,2), (1,3,1), (2,1,1), (2,1,2), (2,2,1), and (3,1,1).