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.*;
public class Main {
    public static void main(String [] args) {
        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong();
        long B = sc.nextLong();
        long gcd = 1;
        gcd = GCD(A,B,gcd);
        ArrayList<Long> List = new ArrayList<Long>();
        for(long i=2;i<=gcd;i++)if(A%i==0&&B%i==0) List.add(i);
        int opt=0;
        for(int i=0;i<List.size();i++){
            ArrayList<Long> set = new ArrayList<>();
            set.add(List.get(i));
            for(int j=i+1;j<List.size();j++) {
                boolean check = true;
                for(int k=0;k<set.size();k++) {
                 if(List.get(j)%set.get(k)==0){
                     check = false;
                     break;
                 }
                }
                if(check) set.add(List.get(j));
            }
            if(opt<set.size()) opt = set.size();
        }
        System.out.println(opt+1);
    }
    public static long GCD(long A,long B,long gcd){
        long r = A%B;
        if(r!=0){
            A = B;
            B = r;
            gcd = GCD(A,B,gcd);
        }
        else gcd = B;
        return gcd;
    }
}