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.ArrayList;
import java.util.Scanner;

public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long a = sc.nextLong();
        long b = sc.nextLong();
        long min = Math.min(a, b);
        long max = Math.max(a, b);
        if (min == 1) {
            System.out.println(1);
            return;
        }
        long gcd = gcd(min, max);
        long cnt = 2;// 1と2
        ArrayList<Integer> list = new ArrayList<>();
        for (int i = 3; i <= gcd; i += 2) {
            if (min % i == 0) {
                list.add(i);
            }
        }
        list.removeIf(i -> {
            return (max % i != 0);
        });
        for (Integer i : list) {
            if (IsPrime(i)) {
                cnt++;
            }
        }
        System.out.println(cnt);
    }

    private static long gcd(long m, long n) {
        if (m < n)
            return gcd(n, m);
        if (n == 0)
            return m;
        return gcd(n, m % n);
    }

    static boolean IsPrime(int n) {
        double sqrtNum = Math.sqrt(n);
        for (int i = 3; i <= sqrtNum; i += 2) {
            if (n % i == 0) {
                return false;
            }
        }
        return true;
    }
}