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)

#define _USE_MATH_DEFINES
#include <bits/stdc++.h>
#define rep(i,n) for(int i = 0; i < (n); i++)
#define divup(a,b) ( ( (a) + ( (b) - 1u) ) / (b) ) // a/b の余り切り上げ
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
// #include <boost/multiprecision/cpp_int.hpp>
// using namespace boost::multiprecision;
ll mod = 1000000007;

ll gcd(ll a,ll b){
    if(a<b) gcd(b,a);
    else{
        if(b==0) return a;
        else return gcd(b,a%b);
    }
}

int main(){
    ll a,b;
    cin>>a>>b;
    ll c=gcd(a,b);
    ll s=1;
    for(int i=2;i*i<=c;i++){
        if(c%i==0){
            while(c%i==0){
                c /= i;
            }
            s++;
        }
    }
    if(c>1) s++;
    cout<<s<<endl;
}