GCD & LCM

Time Limit: Java: 2000 ms / Others: 2000 ms

Memory Limit: Java: 65536 KB / Others: 65536 KB

Description

Given x and y (2 <= x <= 100,000, 2 <= y <= 1,000,000), you are to count the number of p and q such that:

1) p and q are positive integers;

2) GCD(p, q) = x;

3) LCM(p, q) = y.


Input

x and y, one line for each test.


Output

Number of pairs of p and q.


Sample Input

3 60

Sample Output

4

Hint

None

Source

ZOJ Monthly, April 2003

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