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.*;
public class Main {
	
	public static long gcd(long a, long b) {
		return b == 0 ? a: gcd(b, a % b);
	}

	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		long A = sc.nextLong();
		long B = sc.nextLong();
		long C = gcd(A, B);
		long X = (long) Math.sqrt(C);
		List<Integer> p = new ArrayList<>();
		p.add(1);
		p.add(2);
		p.add(3);
		for(int i = 5; i <= Math.sqrt(C); i += 2) {
			boolean isp = true;
			for(int j = 2; j*j <= i; j++) {
				if(i % j == 0) {
					isp = false;
					break;
				}
			}
			if(isp)
				p.add(i);
		}
		int ans = 0;
		for(int i : p) {
			if(C % i == 0) {
				C /= i;
				ans++;
			}
		}
		if(C > X)
			ans++;
		System.out.println(ans);

	}

}