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Count Of Common Divisors

Given two integer numbers, your task is to find count of all common divisors of given numbers

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Count Of Common Divisors

easy

Given two integer numbers, your task is to find count of all common divisors of given numbers

Constraints

1<= t <= 10^5 1<= a, b <= 10^5

Format

Input

The first line contains an integer T, number of test cases. The next t lines contain two numbers a and b each.

Output

Print number of common divisors in next t lines.

Example

Sample Input

3 100000 100000 12 24 747794 238336

Sample Output

36 6 2

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