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.Linq;
using System.Collections.Generic;
using static System.Console;
using System.Text;
using System.IO;
using static System.Math;
namespace AtCoder
{
    class Program
    {
        static public long[] Sarray() { return ReadLine().Split().Select(long.Parse).ToArray(); }
        static public List<long> Slist() { return ReadLine().Split().Select(long.Parse).ToList(); }

        static readonly long Mod = 1000000000 + 7;
        static void Main(string[] args)
        {
            var AB = Sarray();
            var A = AB[0];
            var B = AB[1];
            var g = gcd(A, B);
            var div = primefactorize(g);
            WriteLine(div.Count + 1);
        }
        static long gcd(long x, long y) => y == 0 ? x : gcd(y, x % y);

        static Dictionary<long,long> primefactorize(long n)
        {
            var primes = new Dictionary<long, long>();
            for (long i = 2; i * i <= n; ++i)
            {
                while (n % i == 0)
                {
                    if (primes.ContainsKey(i))
                        ++primes[i];
                    else
                        primes[i] = 1;
                    n /= i;
                }
            }
            if (n != 1) primes[n] = 1;
            return primes;
        }
    }
}