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 Java8 (OpenJDK 1.8.0) (judge verdict: Wrong Answer)

import java.util.*;



public class Main{
  static long gcd (long a, long b) {return b>0?gcd(b,a%b):a;}
  static boolean prime(long n) {

      for(int i = 2; i <=Math.sqrt(n); i++) {
          if(n % i == 0) {
              return false;
          }
      }
      return true;
  }



  public static void main(String[] args){
    Scanner sc = new Scanner(System.in);

    long a = sc.nextLong();
    long b = sc.nextLong();

    long m = gcd(a,b);
    int count =0;
    //ArrayList<Integer> list = new ArrayList<Integer>();

    for(int i=1; i<=(long)Math.sqrt(m)+1; i++){
      if(m%i==0){
        //count += 1;
        if(prime(i)){
          count +=1;
          //System.out.println(i);

        }

      }
    }
    //System.out.println(m);
    //System.out.println(count);
    //System.out.println(list);
    //System.out.println(l);

    System.out.println(count);

  }
}