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.Scanner;
import java.util.stream.Collectors;

public class Main {

	public static void main(String[] args) {
		Scanner scanner = new Scanner(System.in);
		String[] ab = scanner.nextLine().split(" ");
		long a = Long.parseLong(ab[0]);
		long b = Long.parseLong(ab[1]);

		long c = 0;

		long dif = a > b ? a - b : b - a;
		long min = a > b ? b : a;
		long max = dif > min ? min : dif;

		if (a % 2 == 0 || b % 2 == 0) {
			for (long i = 1; i <= max; i++) {
				if (a % i == 0 && b % i == 0) {

					boolean ok = true;
					for (long j = 2; j < i; j++) {
						if (i % j == 0) {
							ok = false;
							break;
						}
					}
					if (ok) {
						c++;
					}
				}
			}
		} else {
			for (long i = 1; i <= max; i++) {
				if (a % i == 0 && b % i == 0) {

					boolean ok = true;
					for (long j = 2; j < i; j++) {
						if (i % j == 0) {
							ok = false;
							break;
						}
					}
					if (ok) {
						c++;
					}
				}
				i++;
			}
		}

		System.out.println(c);
	}
}