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: Time Limit Exceeded)

import java.util.Scanner;
import java.util.ArrayDeque;
import java.util.Deque;
 
class Main {
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
        long a = sc.nextLong();
        long b = sc.nextLong();
        int count = 1;
        long x, y, gcd;
        
        if(a > b){
            x = a;
            y = b;
        }else{
            x = b;
            y = a;
        }
        long temp = -1;
        while(temp != 0){
            temp = x % y;
            x = y;
            y = temp;
        }
        gcd = x;

        for(int i = 2; i*i <= gcd ; i++){
            if(gcd % i == 0)
                count += 1;
            while(gcd % i == 0){
                gcd /= i;
            }
        }
        if(gcd != 1)
            count += 1;

        System.out.println(count);
    }
}