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 <algorithm>

using namespace std;

long yukuriddo(long a, long b) {
	if (a < b) swap(a, b);

	while (a % b > 0) {
		long c = a % b;
		a = b;
		b = c;
	}

	return b;
}

int main()
{
	long a, b;
	cin >> a >> b;
	vector<long> yakusuu;
	yakusuu.push_back(1);
	long pluss[] = { 2,4 };


	long max = yukuriddo(a, b);

	if (max % 2 == 0) {
		max /= 2;
		yakusuu.push_back(2);
		while (max % 2 == 0) max /= 2;
	}
	if (max % 3 == 0) {
		max /= 3;
		yakusuu.push_back(3);
		while (max % 3 == 0) max /= 3;
	}

	//遅いならこの式をどうにかしろ
	int ind = 1;
	for (long index = 5; max > 1; index += pluss[ind]) {
		ind = (ind + 1) % 2;
		if (max % index == 0) {
			max /= index;
			yakusuu.push_back(index);
			while (max % index == 0) max /= index;

		}
	}

	cout << yakusuu.size() << endl;

}