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: Accepted)

#include <bits/stdc++.h>
#include <unordered_set>
using namespace std;
 
unordered_set<long long> sarvesh;
unordered_set<long long> sarvesh2;
unordered_set<long long> sarvesh3;
 
void primeFactors(long long n, unordered_set<long long> &s)
{
s.insert(1);
  while (n%2==0){
    s.insert(2);
    n /= 2;
  }
  for (long long i = 3; i <= sqrt(n); i+= 2){
    while (n%i == 0)
    {
      s.insert(i);
      n /= i;
    }
  }
  if (n > 2)
    s.insert(n);
}
 
int main(){
	long long A, B;
  	scanf("%lld%lld",&A,&B);
  	primeFactors(A, sarvesh);
  	primeFactors(B, sarvesh2);
  	for (auto i = sarvesh.begin(); i != sarvesh.end(); i++) {
        if (sarvesh2.find(*i) != sarvesh2.end()) sarvesh3.insert(*i);
    }
  	cout << sarvesh3.size();
}