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: Time Limit Exceeded)

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 gcd=gcd(a,b);
    List<Long> list=new ArrayList<>();
    long count=0;
    boolean ans=true;

    for(int i=1;i<gcd;i++){
      if(gcd%i==0){
        list.add(gcd/i);
      }
    }

    Iterator it=list.iterator();

    for(long i=0;it.hasNext();i++){
      ans=true;
      Long usagi=(Long)it.next();
      for(int k=2;k<usagi;k++){
        if(usagi%k==0){
          ans=false;
          break;
        }
      }
      if(ans==true){
        count++;
      }
    }
    System.out.println(count+1);

        
   
    }
    static long gcd (long a, long b) {
      long temp;
      while((temp = a%b)!=0) {
        a = b;
        b = temp;
      }
      return b;
    }
}