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: Runtime Error)

using System;
using System.Text;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using static System.Console;
using static System.Math;

public class Program
{
    public static void Main(string[] args)
    {
        new Program().Solve(new ConsoleInput(Console.In, ' '));
    }

    public void Solve(ConsoleInput cin)
    {
        string[] index = ReadLine().Split(' ');
        var a = index[0];
        var b = index[1];
        var count = 0;

        var gcd = Gcd(int.Parse(a), int.Parse(b));

        for (var i = 0; i < gcd; i++)
        {
            if (IsPrime(i))
                count++;
        }
        WriteLine(count);
        ReadKey();
    }

    public static bool IsPrime(int num)
    {
        if (num < 2) return false;
        else if (num == 2) return true;
        else if (num % 2 == 0) return false; // 偶数はあらかじめ除く

        double sqrtNum = Sqrt(num);
        for (int i = 3; i <= sqrtNum; i += 2)
        {
            if (num % i == 0)
            {
                // 素数ではない
                return false;
            }
        }

        // 素数である
        return true;
    }

    public static int Gcd(int a, int b)
    {
        if (a < b)
            // 引数を入替えて自分を呼び出す
            return Gcd(b, a);
        while (b != 0)
        {
            var remainder = a % b;
            a = b;
            b = remainder;
        }
        return a;
    }
}

public class ConsoleInput
{
    private readonly System.IO.TextReader _stream;
    private char _separator = ' ';
    private Queue<string> inputStream;
    public ConsoleInput(System.IO.TextReader stream, char separator = ' ')
    {
        this._separator = separator;
        this._stream = stream;
        inputStream = new Queue<string>();
    }
    public string Read
    {
        get
        {
            if (inputStream.Count != 0) return inputStream.Dequeue();
            string[] tmp = _stream.ReadLine().Split(_separator);
            for (int i = 0; i < tmp.Length; ++i)
                inputStream.Enqueue(tmp[i]);
            return inputStream.Dequeue();
        }
    }
    public string ReadLine { get { return _stream.ReadLine(); } }
    public int ReadInt { get { return int.Parse(Read); } }
    public long ReadLong { get { return long.Parse(Read); } }
    public double ReadDouble { get { return double.Parse(Read); } }
    public string[] ReadStrArray(long N) { var ret = new string[N]; for (long i = 0; i < N; ++i) ret[i] = Read; return ret; }
    public int[] ReadIntArray(long N) { var ret = new int[N]; for (long i = 0; i < N; ++i) ret[i] = ReadInt; return ret; }
    public long[] ReadLongArray(long N) { var ret = new long[N]; for (long i = 0; i < N; ++i) ret[i] = ReadLong; return ret; }
}