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.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 = divisors(g);
            var cnt = 1;//1の分
            foreach (var l in div)
                if (isPrime(l)) ++cnt;
            WriteLine(cnt);

        }
        static long gcd(long x, long y) => y == 0 ? x : gcd(y, x % y);
        static HashSet<long> divisors(long n)
        {
            var div = new HashSet<long>();
            for (var i = 1; i * i < n; ++i)
            {
                if (n % i == 0)
                {
                    div.Add(i);
                    if (i != n / i)
                        div.Add(n / i);
                }
            }
            return div;
        }
        static bool isPrime(long x)
        {
            if (x <= 1) return false;
            if (x == 2) return true;
            if (x % 2 == 0) return false;
            for (var i = 3; i * i <= x; i += 2)
                if (x % i == 0)
                    return false;
            return true;
        }
    }
}