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: Accepted)

using System;
using System.Collections.Generic;
using System.Linq;
using System.IO;
using System.Text;
using static System.Math;
using static System.Array;


namespace AtCoder
{
    class AC
    {
        const int mod = 1000000007;
        const int INF = int.MaxValue / 2;
        const long SINF = long.MaxValue / 2;


        static void Main(string[] args)
        {
            //var sw = new StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false };
            //Console.SetOut(sw);
            var cin = new Scanner();

            var p = cin.SplitReaderL();
            long A = p.Max();
            long B = p.Min();

            long g = GetGcdL(A, B);

            var h = new HashSet<long>();
            h.Add(1);

            for(var i = 2; i <= Sqrt(g); i++)
            {
                while (g % i == 0)
                {
                    g /= i;
                    h.Add(i);
                }
            }
            h.Add(g);

            Console.WriteLine(h.Count());
            
            //Console.Out.Flush();
        }

        struct Edge
        {
            public int _to;
            public long _distance;

            public Edge(int t, long d)
            {
                _to = t;
                _distance = d;
            }
        }

        public static long GetGcdL(long a, long b)
        {
            if (b == 0)
            {
                return a;
            }
            return GetGcdL(b, a % b);
        }


    }
    public class Scanner
    {
        public int[] SplitReader()
        {
            int[] array = Console.ReadLine().Split().Select(int.Parse).ToArray();
            return array;
        }
        public long[] SplitReaderL()
        {
            long[] array = Console.ReadLine().Split().Select(long.Parse).ToArray();
            return array;
        }
    }

   public static class Tool
        {
            static public void Initialize<T>(ref T[] array, T initialvalue)
            {
                for (var i = 0; i < array.Length; i++)
                {
                    array[i] = initialvalue;
                }
            }
            static public long ModuloP(long value, long mod)
            {
                long r = value % mod;

                if (r * mod < 0)
                {
                    r += mod;
                }
                return r;
            }

        }

   struct Pair<T> : IComparable<Pair<T>> where T : IComparable<T>
   {
        public T variable;
        public int index;

        public Pair(T val, int i)
        {
            variable = val;
            index = i;
        }

        public int CompareTo(Pair<T> otherPair)
        {
            return variable.CompareTo(otherPair.variable);
        }

        public int CompareIndex(Pair<T> otherPair)
        {
            return index.CompareTo(otherPair.index);
        }
   }

    


}