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# (.NET Core 3.1.201) (judge verdict: Time Limit Exceeded)

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

namespace AtCoder
{
    class Program
    {
        static long ReadLong()
        {
            return long.Parse(Console.ReadLine());
        }

        static long[] ReadLongs()
        {
            return Console.ReadLine().Split(' ').Select(long.Parse).ToArray();
        }

        static double ReadDouble()
        {
            return double.Parse(Console.ReadLine());
        }

        static double[] ReadDoubles()
        {
            return Console.ReadLine().Split(' ').Select(double.Parse).ToArray();
        }

        static string ReadString()
        {
            return Console.ReadLine();
        }

        static string[] ReadStringSplit()
        {
            return Console.ReadLine().Split(' ');
        }

        static void A()
        {
            var N = ReadLong();
            Console.WriteLine((double)((N + 1) / 2) / (double)N);
        }

        static void B()
        {
            var NK = ReadLongs();
            var N = NK[0];
            var K = NK[1];
            var hs = ReadLongs();
            var ans = 0;
            foreach (var h in hs) {
                if (h >= K)
                {
                    ans++;
                }
            }
            Console.WriteLine(ans);
        }

        static void C()
        {
            var N = ReadLong();
            var A = ReadLongs();
            var ans = new int[N];
            for (int i = 0; i < A.Length; ++i)
            {
                ans[A[i] - 1] = i + 1;
            }
            foreach (var a in ans)
            {
                Console.Write(a + " ");
            }
            Console.WriteLine();
        }

        static HashSet<long> GetPrimeFactors(long a)
        {
            var ret = new HashSet<long>();
            var tmp = a;
            for (int i = 2; i * i <= a; ++i)
            {
                while (tmp % i == 0)
                {
                    ret.Add(i);
                    tmp = tmp / i;
                }
            }

            if (tmp != 1)
            {
                ret.Add(tmp);
            }

            return ret;
        }

        static void D()
        {
            var AB = ReadLongs();
            var A = AB[0];
            var B = AB[1];
            var aPrimeFactors = GetPrimeFactors(A);
            var bPrimeFactors = GetPrimeFactors(B);
            var ans = 0;
            foreach (var a in aPrimeFactors)
            {
                if (bPrimeFactors.Contains(a))
                {
                    ans++;
                }
            }
            Console.WriteLine(ans + 1);
        }

        static void Main(string[] args)
        {
            //A();
            //B();
            //C();
            D();
        }
    }
}