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: Time Limit Exceeded)

#include <stdio.h>

long int gcd(long int a, long int b){
    long int m,n,r;
    if(a > b){
        m = a;
        n = b;
    }else{
        m = b;
        n = a;
    }
    
    while(n != 0){
        r = m % n;
        m = n;
        n = r;
    }
    
    return m;
}

int main(void){
    long int a,b;
    long int gcd_ab;
    long int max, i, pre;
    long int count = 1;
    
    scanf("%ld %ld", &a, &b);
    
    gcd_ab = gcd(a, b);
    i = 2;
    pre = 1;
    while(gcd_ab > 1){
        if(gcd_ab % i == 0){
            if(i != pre){
                count++;
                pre = i;
            }
            gcd_ab = gcd_ab / i;
        }else{
            i++;
        }
    }
    
    printf("%ld\n", count);
    
    return 0;
}