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 9.2.1) (judge verdict: Accepted)

#include <stdio.h>
#define ll long long
ll gcd(ll x,ll y) {
    while(y) {
        ll t=x%y;
        x=y;
        y=t;
    }
    return x;
}

int main()
{
    ll a,b;
    scanf("%lld%lld",&a,&b);
    ll num = gcd(a,b);
    int count=1;
    for (ll i=2;i*i<=num;i++) {
        if (num%i==0) {
            count++;
            while(num%i==0) {
                num/=i;
            }
        }
    }
    printf("%d",count+(num!=1));
    return 0;
}