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 PyPy3 (2.4.0) (judge verdict: Runtime Error)

import math, fractions


def prime_number(n, include_one=True):
    N = n + 1
    table = [0] * N
    
    if include_one:
        prime_list = [1]
    else:
        prime_list = []
    
    for i in range(2, N):
        if table[i] == 0:
            prime_list.append(i)
            
            for j in range(i + i, N, i):
                table[j] = i
    
    return prime_list

def prime_factor(n, include_one=True):
    prime_list = prime_number(n, include_one)
    
    ret = 0
    for i in prime_list:
        if n % i == 0:
            ret +=1
            n /= i
            
    return ret

if __name__ == "__main__":
    A, B = map(int, input().split())
    n = fractions.gcd(A, B)
    print(prime_factor(n))