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.HashSet;
import java.util.List;
import java.util.Scanner;
import java.util.Set;

public class Main {
	public static void main(String[] args) throws Exception {
		Scanner sc = new Scanner(System.in);
		long a = sc.nextLong();
		long b = sc.nextLong();
		sc.close();

		List<Long> list = divList(a, b);
		Set<Long> ans = new HashSet<>();
		for (long o : list) {
			if (isSosuu(o)) {
				ans.add(o);
			}
		}
		System.out.println(ans.size());
	}

	static List<Long> divList(long a, long b) {
		List<Long> list = new ArrayList<>();
		for (long i = 1; i <= 1000000L; i++) {
			if (a % i == 0 && b % i == 0) {
				list.add(i);
			}
		}
		long n = Math.max(a, b);
		for (int i = list.size() - 1; i >= 0; i--) {
			long l = n / list.get(i);
			if (a % l == 0 && b % l == 0) {
				list.add(l);
			}
		}
		return list;
	}

	static boolean isSosuu(long n) {
		long end = (int) Math.sqrt(n);
		for (int i = 2; i <= end; i++) {
			if (n % i == 0) {
				return false;
			}
		}
		return true;
	}
}