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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;
using ll = long long;
#define rep(i, n) for (int i = 0; i < (int)(n); i++)
 
int main() {
  ll a,b,tmp,i,r;
  cin>>a>>b;
  if(a<b){
    tmp = a;
    a = b;
    b = tmp;
  }
  r = a % b;
  while(r!=0){
    a = b;
    b = r;
    r = a % b;
  }
  vector<ll> ans(1);
  ans[0]=1;
  tmp=0;
  if(b!=1){
  for(i=2;;){
    if(i>=b){
        if(ans[ans.size()-1]!=i){
        ans.emplace_back(b);
        }
        break;
    }
    if(b%i==0){
        if(ans[ans.size()-1]!=i){
            ans.emplace_back(i);
            b=b/i;
        }else{
            b=b/i;
        }   
    }else{
        i++;
    }
  }
  cout<<ans.size()<<endl;
  }else{
      cout<<1<<endl;
  }
}