Problem:
Score : 400 points

Problem Statement

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?

Definition of common divisor

An integer d is said to be a common divisor of integers x and y when d divides both x and y.

Definition of being coprime

Integers x and y are said to be coprime when x and y have no positive common divisors other than 1.

Definition of dividing

An integer x is said to divide another integer y when there exists an integer \alpha such that y = \alpha x.

Constraints

All values in input are integers.

1 \leq A, B \leq 10^{12}

Input

Input is given from Standard Input in the following format:

A B

Output

Print the maximum number of divisors that can be chosen to satisfy the condition.

Sample Input 1

12 18

Sample Output 1

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.

Sample Input 2

420 660

Sample Output 2

4

Sample Input 3

1 2019

Sample Output 3

1

1 and 2019 have no positive common divisors other than 1.

Solution in Python (3.4.3) (judge verdict: Wrong Answer)

def main():
    a, b = map(int, input().split(' '))
    d_s = make_divisors(a, b)

    ans = 0
    for d in d_s:

        flg = True
        for j in d_s[1:]:
            if d == j:
                continue
            if d % j == 0:
                flg = False
                break
        if flg:
            ans += 1
    print(ans)


def make_divisors(a, b):
    A = []
    B = []
    n = max(a, b)
    for i in range(1, int(n**0.5)+1):
        if a % i == 0:
            A.append(i)
            if i != a // i:
                A.append(a//i)
        if b % i == 0:
            B.append(i)
            if i != b // i:
                B.append(b//i)
    return list(set(A) & set(B))


if __name__ == '__main__':
    main()