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: Accepted)

# ABC142D - Disjoint Set of Common Divisors
from fractions import gcd
# from math import gcd


def divisors(n: int) -> set:
    div = set()
    for i in range(1, int(n ** 0.5) + 1):
        if n % i == 0:
            div.add(i), div.add(n // i)
    return sorted(div)


def main():
    A, B = map(int, input().split())
    divs = divisors(gcd(A, B))
    divs.pop(0)  # 1 divides all numbers -> pop
    groups = set()
    for i in divs:
        if all(i % x for x in groups):
            groups.add(i)  # coprime to all numbers in "groups"
    ans = len(groups) + 1
    print(ans)


if __name__ == "__main__":
    main()