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

static class CodeJam
{
    static HashSet<long> Divisors(long n)
    {
        var divisors = new HashSet<long> { 1 };
        for (long i = 2; i * i <= n; ++i)
        {
            if (n % i == 0)
            {
                divisors.Add(i);
                while (n % i == 0) { n /= i; }
            }
        }
        if (n > 1) { divisors.Add(n); }
        return divisors;
    }

    static int Solve(long A, long B)
    {
        var d1 = Divisors(A);
        var d2 = Divisors(B);
        return Enumerable.Intersect(d1, d2).Count();
    }

    static void Main(string[] args)
    {
        var V = Array.ConvertAll(Console.ReadLine().Split(), long.Parse);
        Console.WriteLine(Solve(V[0], V[1]));
    }
}