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.Collections.Generic;

namespace AtCoderBeginnerContest142_D
{
    class Program
    {
        static void Main(string[] args)
        {
            string[] ab = Console.ReadLine().Split(' ');
            long A = long.Parse(ab[0]);
            long B = long.Parse(ab[1]);

            List<long> ans = new List<long>();
            long div = CommonDivisor(A, B);
            
            ans.Add(1);
            for(long i = 2; i<div; i++)
            {
                if(A%i==0 & B % i == 0)
                {
                    if(ans.Count == 1 | IsPrime(i) == true)
                    {
                        ans.Add(i);
                    }
                }
            }

            Console.WriteLine(ans.Count);
            //Console.WriteLine(string.Join(' ', ans.ToArray()));
            //Console.ReadKey();
        }

        public static long CommonDivisor(long a, long b)
        {
            if (a < b)
            {
                long tmp = a;
                a = b;
                b = tmp;
            }

            long r = a % b;
            while (r != 0)
            {
                a = b;
                b = r;
                r = a % b;
            }
            return b;
        }

        public static bool IsPrime(long num)
        {
            if (num < 2) return false;
            else if (num == 2) return true;
            else if (num % 2 == 0) return false;
            //else if (num % 3 == 0) return false;

            double sqrtNum = Math.Sqrt(num);
            for(long i = 3; i<= sqrtNum; i += 2)
            {
                if (num % i == 0) return false;
            }
            return true;
        }

    }
}