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.util.ArrayList;
import java.util.HashSet;
import java.util.List;
import java.util.Scanner;

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

        int L = 1 ;
        int S = 1 ;
        int C = 1 ;
        int temp = 1;
        if (a >= b) {
        	L = a;
        	S = b;
        }else {
        	L = b;
        	S = a;
        }

        while (true){
        	temp = S;
        	S = L % S;
        	L = temp;
        	if (S == 0 ) {
        		C = L;
        		break;
        	}
        }
        if (C == 1) {
        	System.out.println(1);
        	return;
        };


        List<Integer> list = new ArrayList<Integer>();
        int num = C;
        int i = 2;

        while (num != 1) {
        	if ( num % i == 0 ) {
        		num = num / i;
        		list.add(i);
        		}
        	 else {
        		i++;
        	}
        }

        List<Integer> ans = new ArrayList<Integer>(new HashSet<>(list));
        System.out.println(ans.size() + 1);
    }
}