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: Runtime Error)

import java.util.*;
public class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
      ArrayList<Integer> list = new ArrayList<Integer>();
		// 整数の入力
		int a = sc.nextInt();
        int b = sc.nextInt();

        //i番目
        
       	int x;
        int y;
        if (a > b) {
            x = a;
            y = b;
        } else {
            x = b;
            y = a;
        }

   
        list.add(1);
        for(int i=2;i<=y;i++){
         if((x%i==0)&&(y%i==0)){
           boolean coprime =true;
           for(int data:list)
             if(list.size()<=1){
              coprime=true;
             break;
             }
             else if(i%data==0 && data!=1){
               coprime =false;
               break;
             }

             if(coprime)list.add(i);
           }

         
        }
      
        //for(int i=0;i<n;i++)
		  // 出力
		for(int data:list)
        System.out.println(data);
	}
}