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: Runtime Error)

#include <iostream>

using namespace std;
#define rep(i, n) for (int i = 0; i < n; i++)
#define rep1(i, s, n) for (int i = s; i <= n; i++)

typedef unsigned long long u8;

u8 gcd(u8 a, u8 b) {
	if (a < b) return gcd(b, a);
	u8 r;
	while ((r = a % b)) {
		a = b;
		b = r;
	}
	return b;
}

int main()
{
	u8 A, B;
	u8 gcdAB;
	u8 max;
	int count = 0;

	cin >> A >> B;

	gcdAB = gcd(A, B);
	bool* flag = new bool[gcdAB + 1];
	for (u8 i = 1; i <= gcdAB; i++) flag[i] = true;

	for (u8 i = 2; i <= gcdAB; i ++) {
		if (flag[i]) {
			for (u8 j = i * 2; j <= gcdAB; j += i) flag[j] = false;
		}
	}

	for (u8 i = 1; i <= gcdAB; i++) if (flag[i] && (gcdAB % i == 0)) count++;
	cout << count << endl;

	delete[] flag;

	return 0;
}