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.ArrayList;
import java.util.List;
import java.util.Scanner;

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

		int num1 = sc.nextInt();
		int num2 = sc.nextInt();

		List<Integer> num1Divisor = new ArrayList<>();
		List<Integer> num2Divisor = new ArrayList<>();
		List<Integer> commonDivisor = new ArrayList<>();

		for(int i = 1;i <= num1; i++) {
			if(num1 % i == 0) {
				num1Divisor.add(i);
			}
		}

		for(int i = 1;i <= num2; i++) {
			if(num2 % i == 0) {
				num2Divisor.add(i);
			}
		}

		for (Integer num : num1Divisor) {
			if(num2Divisor.contains(num)) {

				commonDivisor.add(num);
				for(int i = 2;i<num;i++) {
					if(num % i == 0)
						commonDivisor.remove(num);
				}

			}
		}

		System.out.println(commonDivisor.size());
	}


}