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.HashSet;
import java.util.Scanner;
import java.util.Set;

public class Main {
    public static void main(String[] args) {
        Scanner stdin = new Scanner(System.in);
        int a = stdin.nextInt();
        int b = stdin.nextInt();

        int x = Math.min(a, b);
        int y = Math.max(a, b);
        Set<Integer> cms = new HashSet<>();
        for (int i = 1; i * i <= y; i++) {
            if (y % i != 0) continue;

            int j = y / i;
            if (x % i == 0) cms.add(i);
            if (x % j == 0) cms.add(j);
        }

        int ans = 1;
        for (int cm : cms) {
            if (isPrime(cm)) ans++;
        }

        System.out.println(ans);
    }

    private static boolean isPrime(int x) {
        if (x < 2) return false;
        if (x == 2) return true;
        if (x % 2 == 0) return false;
        for (int i = 3; i * i <= x; i += 2) {
            if (x % i == 0) return false;
        }
        return true;
    }
}