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;

class Program
{
    static void Main(string[] args)
    {
        long[] ab = Console.ReadLine().Split().Select(long.Parse).ToArray();
        long a = ab[0];
        long b = ab[1];

        long gcd = Gcd(a, b);
        List<long> list = new List<long>();
        for (long i = 1; i <= gcd; i++)
        {
            if (a % i == 0 && b % i == 0)
            {
                list.Add(i);
            }
        }
        long count = list.Where(num => IsPrime(num) || num == 1).Count();
        Console.WriteLine(count);
    }

    public static long Gcd(long a, long b)
    {
        if (a < b)
            return Gcd(b, a);

        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }

    public static bool IsPrime(long num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false;

        double sqrtNum = Math.Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                return false;
            }
        }

        return true;
    }
}