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 s = new Scanner(System.in);
        int a = s.nextInt();
        int b = s.nextInt();
        List<Integer> l = new ArrayList<>();
        for (int i = 1; i <= a; i++) {
            if (a % i == 0 && b % i == 0)
                l.add(i);
        }



        for (int i = 0; i < l.size(); i++) {
            if (l.get(i) == 0)
                continue;
            for (int k = 1; k < l.get(i); k++) {
                if (l.get(k) == 0)
                    break;

                if (l.get(i) % 2 == 0 && l.get(k) % 2 == 0) {
                    l.set(i, 0);
                    break;
                }
                if (l.get(i)%k==0) {
                    l.set(i, 0);
                    break;
                }
            }
        }
        int cnt=0;
        for(int i=0;i<l.size();i++){
            System.out.print(l.get(i));
            if(l.get(i)!=0)
                cnt++;
        }
        System.out.print(cnt+1);
    }
}