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: Time Limit Exceeded)


import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
 
public class Main {
    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);

        long A = sc.nextLong();
        long B = sc.nextLong();

        if (A > B) {
            long tmp = B;
            B = A;
            A = tmp;
        }

        List<Long> array = new ArrayList<>();
        List<Long> arrayResult = new ArrayList<>();

        for (long i = 1; i <= A; i++) {
            if ((A % i == 0) && (B % i == 0)) {
                array.add(i);
                arrayResult.add(i);
            }
        }

        for (int i = 1; i < array.size() - 1; i++) {
            for (int j = i + 1; j < array.size(); j++) {
                if (gcd(array.get(i), array.get(j)) != 1) {
                    arrayResult.remove(array.get(j));
                }
            }
        }
        System.out.println(arrayResult.size());
    }

    static long gcd(long x, long y) {
        return y > 0 ? gcd(y, x % y) : x;
    }
 
}