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.io.*;
import java.util.*;

class Main {

    public static void main(String[] args) throws Exception {
        final Scanner sc = new Scanner(System.in);
        long A;
        A = sc.nextLong();
        long B;
        B = sc.nextLong();
        solve(A, B);
    }

    static void solve(long A, long B){
        long tmp;
        while ((tmp = A % B) != 0) {
            A = B;
            B = tmp;
        }
        long ans = 1;

        if(B%2==0) {
            while(B%2==0) {
                B /= 2;
            }
            ans++;
        }

        long i = 3;
        while (B >= i) {
            if(B%i==0) {
                while(B%i==0) {
                    B /= i;
                }
            }
            i += 2;
        }

        System.out.println(ans);


    }
}