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>

long gcd(long A, long B) {
    while (B != 0) {
        long tmp = A;
        A = B;
        B = tmp % B;
    }
    return A;
}

int main() {
    long A = 0, B = 0;
    if (scanf("%ld%ld", &A, &B) != 0) {
        long GCD = gcd(A, B);
        int sumOfDivisors = 1;
        long i = 2;
        while (i <= sqrt(GCD)) {
            int flag = 1;
            while (GCD % i == 0) {
                GCD /= i;
                if (flag == 1) {
                    sumOfDivisors++;
                    flag = 0;
                }
            }

            ++i;
        }
        if (GCD != 1) {
            sumOfDivisors++;
        }

        printf("%d", sumOfDivisors);
    }

    return 0;
}