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.Scanner;
import java.util.ArrayList;

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

    	ArrayList<Integer> list = new ArrayList<>();
        for(int i = 1; i <= a && i <= b; i++){
          if(a%i == 0 && b%i == 0) list.add(i);
        }
    
		int[] check = new int[list.size()];
    	for(int i = 1; i < list.size()-1; i++){
        	for(int j = i+1; j < list.size(); j++){
            	if(list.get(j) % list.get(i) == 0) check[j] = 1;
            }
        }
    	int count = 0;
    	for(int i = 0; i < list.size(); i++)
          if(check[i] == 0) count++;
    	System.out.println(count);
    }
}