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.Diagnostics;
using System.IO;
using System.Text;
using System.Linq;
using System.Collections.Generic;

class Program
{
    static void Main(string[] args) {
#if DEBUG
        //MyDebugger.MakeTestCase("../TextFile2.txt");
        MyDebugger.Test(process, "../TextFile1.txt");
#else
        object ret = process(new StreamReader(Console.OpenStandardInput()));
        Console.WriteLine(ret);
#endif
    }

    static object process(TextReader input) {
        var spl   = input.ReadLine().Split(' ');
        long a    = long.Parse(spl[0]);
        long b    = long.Parse(spl[1]);

        var ab = calc(a, b);

        return ab.Count();
    }

    static List<long> calc(long a, long b) {
        List<long> list = new List<long>();
        long n = Euc(a, b);
        for(long i=1; i<=n; i++) {
            if (a % i == 0 && b % i == 0) {
                bool ok = true;
                foreach (var l in list) {
                    if(l!=1 && i%l == 0) {
                        ok = false;
                        break;
                    }
                }
                if (ok) {
                    list.Add(i);
                }
            }
        }
        return list;
    }

    static long Combination(long m, long n) {
        if (m == n || n == 0) return 1;

        long ans = 1;
        for (long i = 1; i <= n; i++) {
            ans = ans * (m - i + 1) / i;
        }
        return ans;
    }

    static long Euc(long m, long n) {
        if (m < n) {
            var t = m;
            m = n;
            n = t;
        }

        while (true) {
            var mod = m % n;
            if (mod == 0) return n;
            m = n;
            n = mod;
        }
    }
}