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: Accepted)

import java.util.*;

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

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

      long ans = 1;

      long gcdab = euku(a,b);

      int n = (int)Math.sqrt(gcdab);

      for(int i=2;i<=n;i++){
        if(gcdab%i==0){
          ans++;
          while(gcdab%i==0){
            gcdab /= i;
          }
        }
      }

      if(gcdab!=1){
        ans++;
      }

      System.out.println(ans);

    }

    public static long euku(long a,long b){

      if(a%b!=0){
        return euku(b,a%b);
      }
      else{
        return b;
      }

    }

}