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) throws Exception {
        Scanner sc = new Scanner(System.in);
        long A = Long.parseLong(sc.next());
        long B = Long.parseLong(sc.next());
        long max = Math.max(A,B);
        long min = Math.min(A,B);
        ArrayList<Long> list = new ArrayList<>();
        list.add(1L);
        long sosu = 0;
        for(long i=2; i<=Math.sqrt(min); i++) {
            if(max % i == 0) {
                if(min % i == 0) {
                    if(sosuu(i) && (list.contains(i) == false)) {System.out.println(i);sosu++;}
                    list.add(i);
                }
                if(min % (max/i) == 0) {
                    if(sosuu(max/i) && (list.contains(max/i) == false)) {System.out.println(min/i);sosu++;}
                    list.add(max/i);
                }
            }
        }
        
        if(sosuu(A) && sosuu(B) && A == B) sosu++;
        System.out.println(sosu+1);
    }

    public static boolean sosuu(long n) {
        for(long i = 2; i <= Math.sqrt(n); i++) {
            if(n % i == 0) {
                return false;
            }
        }
        return true;
    }
}