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.ArrayList;

class Main{
    public static void main(String[] args){
        
        Scanner sc = new Scanner(System.in);
 
        long A = sc.nextLong();
        long B = sc.nextLong();
        
        ArrayList<Integer> lista = new ArrayList<Integer>();
        for(int i=2; i<=1000000; i++){
            if(A%i==0){
                lista.add(i);
                A = A / i;
                i--;
            }
        }
        ArrayList<Integer> listb = new ArrayList<Integer>();
        for(int i=2; i<=1000000; i++){
            if(B%i==0){
                listb.add(i);
                B = B / i;
                i--;
            }
        }
        System.out.println(lista);
        System.out.println(listb);
        int ans = 0;
        for(int i=0; i<listb.size(); i++){
            if(lista.contains(listb.get(i))){
                if(i>0 && listb.get(i)!=listb.get(i-1)){
                    ans += 1;
                }
                if(i==0){
                    ans += 1;
                }
                lista.remove(lista.indexOf(listb.get(i)));
            }
        }
        System.out.println(ans + 1);
    }
}