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;
using System.Text;
using System.Threading.Tasks;

namespace ConsoleApp1
{
    static class DDisjointSetofCommonDivisors
    {
        static void Main(string[] args)
        {
            var ab = Console.ReadLine().Split(' ').Select(x => long.Parse(x)).ToList();
            long a = ab[0];
            long b = ab[1];

            long gcd = Gcd(a, b);

            var answerList = new List<long>();
            for (int i = 1; i <= gcd; i++)
            {
                if (gcd % i > 0)
                {
                    continue;
                }
                if (!answerList.Any(x => Gcd(x, i) > 1))
                {
                    answerList.Add(i);
                }                
            } 

            Console.WriteLine(answerList.Count());
            Console.ReadLine();
        }

        static long Gcd(long a, long b)
        {
            if (a < b)
            {
                return Gcd(b, a);
            }
            if (a % b == 0)
            {
                return b;
            }
            return Gcd(b, a % b);
        }
    }
}