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.Arrays;
import java.util.Scanner;

public class Main {

    static long gcd(long a, long b) {
        if (a > b) return gcd(b, a);
        if (a == 0) return b;
        return gcd(b % a, a);
    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        long A = sc.nextLong();
        long B = sc.nextLong();
        long d = gcd(A, B);

        boolean[] prime = new boolean[(int) Math.ceil(Math.sqrt(d)) + 1];
        Arrays.fill(prime, true);

        int sol = 1;
        for (int i = 2; i < prime.length; i++) {
            if (!prime[i]) continue;
            if (d % i == 0) sol++;
            for (int j = i; j < prime.length; j += i) prime[j] = false;
        }

        if (sol == 1) sol = d == 1 ? 1 : 2;
        System.out.println(sol);
    }
}