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 (GCC 5.4.1) (judge verdict: Accepted)

#include <stdio.h>
#include <math.h>
#include <stdlib.h>
long long gcd(long long a,long long b){
    if(a<b){
        long long tmp=a;
        a=b;
        b=tmp;
    }
    long long r=a%b;
    while(r>0){
        a=b;
        b=r;
        r=a%b;
    }
    return b;
}
int main()
{   
    long long a,b;
    scanf("%lld%lld",&a,&b);
    long long  max=gcd(a,b);
    long long ans=1;
    for(long long i=2;i*i<=max;i++){
        if(max%i==0){
            ans++;
            while(max%i==0){
                max/=i;
            }
        }
    }
    if(max>1)ans++;
    printf("%lld",ans);
    return 0;
}