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)

package antbook.p0;

import java.util.Scanner;

public class Main {

    long a;
    long b;

    Main(long a, long b) {
        this.a = a;
        this.b = b;
    }

    /**
     * 
     * @return greeting message
     */
    public int solve() {

        // max integer requred
        int UPPER_BOUND = (int) (Math.sqrt(Math.max(a, b)));

        // prime sieve
        boolean[] isPrime = new boolean[UPPER_BOUND];

        // prime list
        int[] plist = new int[UPPER_BOUND];

        isPrime[0] = false;
        isPrime[1] = false;
        for (int i = 2; i < UPPER_BOUND; i++) {
            isPrime[i] = true;
        }

        int c = 0;
        for (int i = 2; i < UPPER_BOUND; i++) {
            if (isPrime[i]) {
                plist[c++] = i;
                for (int j = i * 2; j < UPPER_BOUND; j += i) {
                    isPrime[j] = false;
                }
            }
        }

        int ans = 1;

        for (int i = 0; i < c; i++) {
            if (a % plist[i] == 0 && b % plist[i] == 0) {
                ans++;
            }
        }

        return ans;
    }

    public static void main(String[] args) {

        // input
        Scanner sc = new Scanner(System.in);
        long a = sc.nextLong();
        long b = sc.nextLong();
        sc.close();

        // solve
        int p = new Main(a, b).solve();

        // display
        System.out.println(p);
    }

}