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: Wrong Answer)

using System;
using System.Linq;
using System.Collections.Generic;
namespace mytest
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = Console.ReadLine();
            var A = Int64.Parse(input.Split(' ')[0]);
            var B = Int64.Parse(input.Split(' ')[1]);

            Int64 a = Gcd(A,B);
          　var la = new List<Int64>();
            Int64 total = 0;
            if(a == 1)
            {
              total = 1;
            }
            else
            {
              　Int64 b = a;
                while(true)
                {
                    if (a % b == 0)
                    {
                        if (IsPrime(b)) total += 1;
                    }
                    if (b == 1) break;
                    else b = (Int64)Math.Ceiling((double)b / 2);
                }                
            }
            Console.WriteLine(total);
        }
      
      　public static Int64 Gcd(Int64 a, Int64 b)
        {
            Func<Int64, Int64, Int64> gcd = null;
            gcd = (x, y) => y == 0 ? x : gcd(y, x % y);
            return a > b ? gcd(a, b) : gcd(b, a);
        }
      
      　private static bool IsPrime(Int64 num)
        {
         　 if (num == 2)
            {
                return true;
            }
         　 if (num % 2 == 0)
            {
                return false;
            }

            for (var i = 3; i < num; i += 2)
            {
                if (num % i == 0)
                {
                    return false;
                }
            }

            return true;
        }
    }
}