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 C++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

    #include <cstring>
    #include <memory>
    #include <algorithm>
    #include <iostream>
    #include <mutex>
    #include <limits>
     
    #include <iomanip>
    #include <cmath>
    #include <string>
     
     
    #include <iostream>
    #include <vector>
    #include <utility>
    #include <algorithm>
    #include <cmath>
    #include <numeric>
     
    int main () {
    	unsigned long long A;
      	unsigned long long B;
      
      	std::cin >> A;
      	std::cin >> B;
      
      	auto gcd = std::__gcd(A, B);
     	
      	int count = 1;
      
      	auto tmp = gcd;
      	for(unsigned long long i=2; i<std::sqrt(gcd)+1; ++i) {
         	if(tmp % i ==0) {
              ++count;
              while(tmp%i == 0)
                tmp /= i;
            }
        }
      
      std::cout << count;
    }