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  1. Practice
  2. Mathematics
  3. Geometry
  4. Sherlock and Counting

Sherlock and Counting

Watson gives Sherlock two integers, and , and asks him to count the number of positive integer 's such that:

Given queries where each query consists of some and , print the number of possible 's for each query on a new line.

Input Format

The first line contains an integer, , denoting the number of times Watson queries Sherlock.
Each of the subsequent lines contains two space-separated integers denoting the respective values of and for a query.

Constraints

Output Format

For each query, print the number of 's satisfying the given formula on a new line.

Sample Input

2
5 1
5 2

Sample Output

2
4

Explanation

Sherlock performs the following queries:

  1. The possible values of satisfying Watson's formula for and are and . Because there are two such values, we print on a new line.
  2. The possible values of satisfying Watson's formula for and are , , , and . Because there are four such values, we print on a new line.