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.Arrays;
import java.util.HashSet;
import java.util.Scanner;

public class Main {

    int MAX = 1000000;
    boolean[] primes;

    void run() {
        Scanner sc = new Scanner(System.in);
        long A = sc.nextLong(), B = sc.nextLong();

        long x = gcd(A, B);

        HashSet<Long> y = new HashSet<>();

        for (long i = 2; i * i <= x; i++) if (x % i == 0){
            y.add(i);
            y.add(x / i);
        }
//        debug(y.size(), y);

        int ans = 0;
        for (long i : y) {
            if (isPrime(i)) ans++;
        }

        if (isPrime(x)) ans++;

        System.out.println(ans + 1);
    }

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

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

    void debug(Object... os) {
        System.err.println(Arrays.deepToString(os));
    }

    public static void main(String[] args) {
        new Main().run();
    }

}