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.*;

public class Main{
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);

        long a = sc.nextLong();
        long b = sc.nextLong();

        long tmp = 0;
        while ((tmp = a % b) != 0){
            a = b;
            b = tmp;
        }

//        System.out.println(b);

        long ans = 0;

//        boolean flag = false;

//        if (b%2==0) ans++;

//        for (int i=2; i*i<=b; i++){
//            if (b%i==0){
//                ans++;
//                while (b%i==0){
//                    b /= i;
//                }
//            }
//        }


        if (b%2==0 || b%3==0 || b%5==0 || b%7==0){
            for (int i=2; i<=b; i++){
                if (b%i==0){
                    ans++;
                    while (b%i==0){
                        b /= i;
                    }
                }
            }
        }else{
            for (int i=2; i*i<b; i++){
                if (b%i==0){
                    ans++;
                }
            }
        }


        System.out.println(ans+1);
    }
}