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 static System.Math;
using System.Collections.Generic;

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


            var gcdAB = GCD(A, B);


            var cd = new List<long>();


            //公約数をリストアップ
            for (int i = 1; i <= gcdAB; i++)
            {
                if (A % i == 0 && B % i == 0)
                {
                    cd.Add(i);
                }
            }

            var ans = new List<long>(cd);
            
            //公約数の中から、互いに素なもの(=素数)のみを残す。
            foreach(var x in cd)
            {
                if(!isPrime(x))
                {
                    ans.Remove(x);
                }
            }

            //1は素数でないので、追加する。
            ans.Add(1);

            Console.Write(ans.Count()+1);

        }

        static bool isPrime(long x)
        {
            if(x < 2) return false;
            else if(x == 2) return true;
            else if(x%2 == 0) return false;

            double sqrtX = Math.Sqrt(x);

            for(int i=3;i<sqrtX;i+=2)
            {
                if(x %i == 0)
                {
                    return false;
                }
            }
            return true;
        }


        static long LCM(long m, long n)
        {
            return m / GCD(m, n) * n; 
        }

        static long GCD(long m, long n)
        {
            while (true)
            {
                if (n == 0) return m;
                m %= n;
                if (m == 0) return n;
                n %= m;
            }
        }
    }

}