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: Time Limit Exceeded)

using System;
using System.Collections.Generic;
using System.Linq;

namespace test
{
    class Program
    {
        static void Main(string[] args)
        {
            var input = ReadArrayLong();
            var A = input[0];
            var B = input[1];
            var comD = Gcd(A, B);
            var pri = PrimeList(comD);
            var cnt = 1L;
            var idx = 0;
            while (comD != 1)
            {
                var first = false;
                while (comD % pri[idx] == 0)
                {
                    comD /= pri[idx];
                    if (!first)
                    {
                        cnt++;
                        first = true;
                    }
                }
                idx++;
            }

            Console.WriteLine(cnt);
            Console.ReadLine();
        }

        static long Gcd(long a, long b) { if (b == 0) return a; return Gcd(b, a % b); }
        static List<long> PrimeList(long num)
        {
            var pri = new List<long>();
            pri.Add(2);

            for (var i = 3; i <= num; i += 2)
            {
                var prime = true;
                for (var j = 3; j <= Math.Sqrt(i); j += 2)
                {
                    if (i % j == 0)
                    {
                        prime = false;
                        break;
                    }
                }
                if (prime) pri.Add(i);
            }

            return pri;
        }

        static string Read() { return Console.ReadLine(); }
        static int ReadInt() { return int.Parse(Read()); }
        static long ReadLong() { return long.Parse(Read()); }
        static int[] ReadArrayInt() { return Read().Split(' ').Select(s => int.Parse(s)).ToArray(); }
        static long[] ReadArrayLong() { return Read().Split(' ').Select(s => long.Parse(s)).ToArray(); }
    }
}