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: Wrong Answer)

#include <bits/stdc++.h>

using Int = unsigned long long;
using namespace std;

#define ARC(i, a, b) for(Int i = (a); i < (b); ++i)
#define RC(i, n) ARC(i, 0, n)
#define ARCH(i, a, b) for(Int i = (a) - 1; i >= (b); --i)
#define RCH(i, n) ARCH(i, n, 0)
template<class T> T ant(const T &a, const T &b){ return a > b ? a : b; };
template<class T> T ont(const T &a, const T &b){ return a < b ? a : b; };
template<class T> T th(T &a, const T &b, T (*f)(const T &, const T &)){ a = f(a, b); }
#define anth(a, b) th(a, b, ant)
#define onth(a, b) th(a, b, ont)

int main(){
	Int a, b;
	cin >> a >> b;
	while(b) b = a % (a = b);

	Int cnt = 1;

	for(Int i = 2; i <= a; ++i){
		if(a % i == 0){
			++cnt;
			while(a % i == 0) a /= i;
		}
	}

	cout << cnt << endl;
}