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.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;

public class Main {
    public static void main(String args[]) throws Exception{
        BufferedReader stdR = new BufferedReader(new InputStreamReader(System.in));
        String[] s = stdR.readLine().split(" ");
        int a = Integer.parseInt(s[0]);
        int b = Integer.parseInt(s[1]);
        int N = gcd(a, b);
        
        int count = 1;
        if(N % 2 != 1 && N >= 2)count++;
        for(int i = 3 ; i <= N ; i+= 2) {
            boolean prime = true;
            if(a % i != 0 || b % i != 0)continue;
            for(int j = 3 ; j <= Math.sqrt(i) ; j++) {
                if(i % j == 0) {
                    prime = false;
                    break;
                }
            }
            if(prime)count++;
        }
        System.out.println(count);
    }
    
    public static int gcd(int a, int b) {
        if(b == 0)return a;
        return gcd(b, a % b);
    }
}