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 <iostream>
#include <vector>
#include <queue>

int calc_gcd(int a, int b) {
  if (a == b)
    return a;
  
  if (a == 1 || b == 1)
    return 1;
  
  return (b < a) ? calc_gcd(b, a-b) : calc_gcd(a, b-a);
}

void list_cd(int gcd, std::vector<int>& vec) {
  vec.push_back(1);
  for (int i=2; i<=gcd; ++i) {
    if (gcd % i == 0) vec.push_back(i);
  }
}

int main() {
  int A, B;
  std::cin >> A >> B;
  
  auto gcd = calc_gcd(A, B);
  
  std::vector<int> vec;
  list_cd(gcd, vec);
  
  std::deque<bool> deque(gcd, true);
  
  for (auto &&e : vec) {
    if (e > 1)  {
      for (auto i=e*2; i<=gcd; i+=e) {
        deque[i-1] = false;
      }
    }
  }
  int ans = 0;
  for (auto &&e : vec) {
    if (deque[e-1]) ++ans;
  }
  std::cout << ans << std::endl;
}