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 <bits/stdc++.h>
using namespace std;
typedef long long int ll;
int main() {
    ll a,b,t1,t2,i,j,temp=0,flag=0,count=1;
    cin>>a>>b;
    t1=min(a,b);
    t2=max(a,b);
    for(i=2;i*i<=t1;i++)
    {
        temp=0;
        flag=0;
        if(t1%i==0)
        {
            if(t2%i==0||t2%(t1/i)==0)
            {
            if(t2%i==0)
            temp=i;
            else
            temp=t1/i;
            }
            

            if(temp!=0)
            {
                for(j=2;j*j<=temp;j++)
                {
                    if(temp%j==0)
                    {
                        flag=1;break;
                    }
                }
                if(flag==0)
                count++;
            }

        }
    }
    cout<<count;
    
 
     

  return 0;
    
}