Description

Given two positive integers $x_0, y_0$, find the number of pairs $P, Q$ that satisfy the following conditions:

1. $P, Q$ are positive integers.
2. $P, Q$ have greatest common divisor $x_0$ and least common multiple $y_0$.

Compute the number of all possible pairs $(P, Q)$ that satisfy the conditions.

Input Format

One line with two positive integers $x_0, y_0$.

Output Format

One line with a single number, representing the number of pairs $P, Q$ that satisfy the conditions.

3 60

4

Hint

There are 4 possibilities for $P, Q$:

1. $3, 60$.
2. $15, 12$.
3. $12, 15$.
4. $60, 3$.

Constraints: For $100\%$ of the testdata, $2 \le x_0, y_0 \le 10^5$.

Source: NOIP 2001 Junior, Problem 2.

Translated by ChatGPT 5