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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <queue>
#include <stdlib.h>
#include <map>
#include <cmath>
#define MOD_P 1000000007
#define ll long long
using namespace std;

ll gcd(ll a, ll b)
{
	if (a % b == 0) {
		return b;
	}
	return gcd(b, a % b);
}

int main()
{
	ll a, b;
	cin >> a >> b;
	ll g = gcd(a, b);
	int size = 0;
	ll ans = 1LL;

	//printf("gcd=%lld\n", g);
	ll i = 1LL;

	while (g > 1LL) {
		if (i != 1LL && g % i == 0) {
			//printf("%lld/%lld\n", g, i);
			g /= i;
		} else {
			while (i == 1LL || g % i != 0) {
				//printf("[i=%lld] ", i);
				i++;
			}
			//printf("ans++(%lld)(i=%lld)\n", ans, i);
			ans++;
		}
	}

	printf("%lld", ans);

	return 0;
}