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: Accepted)

import java.util.Scanner;

/**
 * Disjoint Set of Common Divisors
 */
public class Main {

    public static void main(String[] args) throws Exception {
        try (Scanner sc = new Scanner(System.in)) {
            long A = sc.nextLong();
            long B = sc.nextLong();

            long gcd = gcd(A, B);

            long ans = 0;

            for (long d = 1; d * d <= gcd; d++) {
                if (gcd % d != 0) {
                    continue;
                }

                if (isPrime(d)) {
                    ans++;
                }

                if (gcd / d != d && isPrime(gcd / d)) {
                    ans++;
                }
            }

            System.out.println(ans);
        }
    }

    static long gcd(long M, long N) {
        if (M < N) {
            return gcd(N, M);
        }
        return N > 0 ? gcd(N, M % N) : M;
    }

    static boolean isPrime(long N) {
        for (long i = 2; i * i <= N; i++) {
            if (N % i == 0) {
                return false;
            }
        }
        return true;
    }

}