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 C# (Mono 4.6.2.0) (judge verdict: Time Limit Exceeded)

using System;
using System.Linq;
using System.Collections.Generic;
using System.Text;

namespace AtCoder
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] input = Console.ReadLine().Split(' ');
            long A = long.Parse(input[0]);
            long B = long.Parse(input[1]);
            long gcd_val = Gcd(A, B);
            long count = 1;
            List<long> atom_list = new List<long>();
            List<int> remove_index = new List<int>();
            if (gcd_val != 1)
            {
                for (int i = 1; i <= gcd_val; i++)
                {
                    if (gcd_val % i == 0)
                    {
                        count++;
                        atom_list.Add(i);
                    }
                }
                for (int i = 1; i < atom_list.Count; i++)
                {
                    for (int j = 1; j < i; j++)
                    {
                        if (atom_list[i] % atom_list[j] == 0 && !remove_index.Contains(i)) remove_index.Add(i);
                    }
                }
                Console.WriteLine((atom_list.Count - remove_index.Count).ToString());
            }
            else Console.WriteLine("1");

//            Console.Read();
        }
        // Gratest Common Divider by Euclid 
        public static long Gcd(long a, long b)
        {
            if (a < b)
                return Gcd(b, a);
            while (b != 0)
            {
                var remainder = a % b;
                a = b;
                b = remainder;
            }
            return a;
        }
    }
}