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: Wrong Answer)

#include <stdio.h>
#define ll long long

int ll GCD(int ll x, int ll y) {
	if (y == 0) return x;
	return GCD(y, x % y);
}

int factorize(int ll n) {
	int ll i;
	int cnt = 0;
	int num = n;
	for (i = 2; i < num; i++) {
		if (n % i != 0) continue;
		cnt++;
		while (n % i == 0) {
			n /= i;
		}
	}
	return cnt;
}

int main() {
	int ll A, B;

	scanf("%lld %lld", &A, &B);
	int ll g = GCD(A, B);

	int f = factorize(g);

	printf("%d", f + 1);

	return 0;
}