Hdu 4497 GCD and LCM (number theory & combinatorial mathematics)

GCD and LCM

http://acm.hdu.edu.cn/showproblem.php?pid=4497

Time limit:2000/1000 MS (java/others)

Memory limit:65535/65535 K (java/others)

Problem Description

Given two positive integers G and L, could you tell me how many solutions of (x, Y, z) There are, satisfying that gcd (x, y , z) = G and LCM (x, y, z) = L?

Note, gcd (x, y, z) means the greatest common divisor of x, Y and Z, while LCM (x, y, z) means the least common multiple of x, Y and Z.

Note 2, (1, 2, 3) and (1, 3, 2) are two different solutions.

Input

The comes an integer t (t <=), telling the number of test cases.

The next T lines, each contains two positive 32-bit signed integers, G and L.

It's guaranteed that each answer would fit in a 32-bit signed integer.

Output

For the all test case, print one line with the number of solutions satisfying the conditions above.

Sample Input

2 6 72 7 33

Sample Output

72 0

Source