Score : 400 points
Given are positive integers A and B.
Let us choose some number of positive common divisors of A and B.
Here, any two of the chosen divisors must be coprime.
At most, how many divisors can we choose?
An integer d is said to be a common divisor of integers x and y when d divides both x and y.
Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.
An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.
Input is given from Standard Input in the following format:
A B
Print the maximum number of divisors that can be chosen to satisfy the condition.
12 18
3
12 and 18 have the following positive common divisors: 1, 2, 3, and 6.
1 and 2 are coprime, 2 and 3 are coprime, and 3 and 1 are coprime, so we can choose 1, 2, and 3, which achieve the maximum result.
420 660
4
1 2019
1
1 and 2019 have no positive common divisors other than 1.