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.*;
import java.util.stream.Stream;

public class Main {

    List<Integer> kouyaku = new ArrayList<Integer>();

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        String str  = sc.nextLine();
        String[] astr = str.split(" "); //状況に合わせて
        int[] in_data = Stream.of(astr).mapToInt(x->{
            try{
                return Integer.parseInt(x);
            }
            catch(Exception e){
                e.printStackTrace();
            }
            return 0;
        }).toArray();
        sc.close();
        int a = in_data[0];
        int b = in_data[1];
        if(a == 1 | b==1){
            System.out.println("1");
            System.exit(0);
        }

        List<Integer> kouyaku = new ArrayList<Integer>();
        List<Integer> ans = new ArrayList<Integer>();
        for(int i=1;i<a;i++){
            if(a%i == 0 && b%i== 0){
                kouyaku.add(i);
            }
        }
        for(int j=0;j<kouyaku.size();j++){
            for(int m=j+1;m<kouyaku.size();m++){
                if(check(kouyaku.get(j),kouyaku.get(m)) == true ){
                    if(ans.indexOf(kouyaku.get(j)) == -1){
                        ans.add(kouyaku.get(j));
                    }
                    if(ans.indexOf(kouyaku.get(m)) == -1){
                        ans.add(kouyaku.get(m));
                    }
                }
                else if(check(kouyaku.get(j),kouyaku.get(m)) == false){
                    int index = ans.indexOf(kouyaku.get(j));
                    if(index != -1){
                        ans.remove(index);
                    }
                    int index2 = ans.indexOf(kouyaku.get(m));
                    if(index2 != -1){
                        ans.remove(index2);
                    }
                }
                }
            }
        System.out.println(ans.size());
        }


    public static Boolean check(Integer a, Integer b){
        for(int l = 2;l<a;l++){
            if(a%l == 0 && b%l ==0){
                return false;
            }
        }
        return true;
    }
}