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: Wrong Answer)

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

class Program
{
    static void Main()
    {
        var input = ReadLongs();
        var n = input[0];
        var m = input[1];

        var x = Gdc(n, m);
        var ret = GeneratePrime((int)Math.Sqrt(x)+1).Count(p => x % p == 0) + 1;
        Console.WriteLine(ret);
    }


    static private IEnumerable<int> BitStands(int bit)
    {
        for (int i = 0 ; bit > 0; bit >>= 0,i++)
        {
            if ((bit & 1) > 0) yield return i;
        }
    }

    private static long Gdc(long a, long b)
    {

        /* 自然数 a > b を確認・入替 */
        if (a < b)
        {
            var tmp = a;
            a = b;
            b = tmp;
        }

        /* ユークリッドの互除法 */
        var r = a % b;
        while (r != 0)
        {
            a = b;
            b = r;
            r = a % b;
        }
        return b;
    }


    private static List<int> GeneratePrime(int max)
    {
        if (max == 1) return new List<int>() {};
        int prime;
        double sqrtMax = Math.Sqrt(max);
        var primeList = new List<int>();

        var searchList = Enumerable.Range(2, max - 1).ToList();

        do
        {
            prime = searchList.FirstOrDefault();
            if (prime == 0) break;
            primeList.Add(prime);
            searchList.RemoveAll(n => n % prime == 0);

        } while (prime < sqrtMax);

        primeList.AddRange(searchList);

        return primeList;
    }
    #region Utils
    static int[] ReadInts()
    {
        return Console.ReadLine().Split().Select(int.Parse).ToArray();
    }
    static long[] ReadLongs()
    {
        return Console.ReadLine().Split().Select(long.Parse).ToArray();
    }
    #endregion
}