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

public class Main {

    public static void main(String[] args) {

        Scanner in = new Scanner(System.in);
        String[] params = in.nextLine().split(" ");
        long a = Long.parseLong( params[0]);
        long b = Long.parseLong( params[1]);

        long count = a < b ? a : b;
        for( long i = count ; 0 < i ; i-- ){
            // 公約数か確認
            if( a % i == 0 && b % i == 0 ){

                List<Long> primes = new ArrayList<>();
                long temp = 1;
                primes.add(temp);

                for( long j = 2 ; j <= i ;){
                    if( i % j == 0 ){
                        if( primes.get(primes.size()-1) != j ){
                            primes.add( j );
                        }
                        i /= j;
                    }
                    else {
                        j++;
                    }
                }

                System.out.println( primes.size() );
                return;
            }
        }
        System.out.println( 1 );

    }

}