Problem:
Score : 500 points

Problem Statement

Snuke is conducting an optical experiment using mirrors and his new invention, the rifle of Mysterious Light.

Three mirrors of length N are set so that they form an equilateral triangle.
Let the vertices of the triangle be a, b and c.

Inside the triangle, the rifle is placed at the point p on segment ab such that ap = X.
(The size of the rifle is negligible.)
Now, the rifle is about to fire a ray of Mysterious Light in the direction of bc.

The ray of Mysterious Light will travel in a straight line, and will be reflected by mirrors, in the same ways as "ordinary" light.
There is one major difference, though: it will be also reflected by its own trajectory as if it is a mirror!
When the ray comes back to the rifle, the ray will be absorbed.

The following image shows the ray's trajectory where N = 5 and X = 2.

It can be shown that the ray eventually comes back to the rifle and is absorbed, regardless of the values of N and X.
Find the total length of the ray's trajectory.

Constraints

2≦N≦10^{12}

1≦X≦N-1

N and X are integers.

Partial Points

300 points will be awarded for passing the test set satisfying N≦1000.

Another 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N X

Output

Print the total length of the ray's trajectory.

Sample Input 1

5 2

Sample Output 1

12

Refer to the image in the Problem Statement section.
The total length of the trajectory is 2+3+2+2+1+1+1 = 12.

Solution in C# (Mono 4.6.2.0) (judge verdict: Wrong Answer)

﻿using System;
﻿using System.Globalization;
﻿using System.IO;
﻿using System.Linq;

namespace CF317
{
    internal class Program
    {
        private static void Main(string[] args)
        {
            var sr = new InputReader(Console.In);
            //var sr = new InputReader(new StreamReader("input.txt"));
            var task = new Task();
            using (var sw = Console.Out)
            //using (var sw = new StreamWriter("output.txt"))
            {
                task.Solve(sr, sw);
                //Console.ReadKey();
            }
        }
    }

    internal class Task
    {
        public void Solve(InputReader sr, TextWriter sw)
        {
            var input = sr.ReadArray(Int64.Parse);
            var n = input[0];
            var x = input[1];
                var result = x;
                var len = n - (n - x);
                if (len % (n - x) == 0) {
                    result += 2*len / (n - x);
                }
                else {
                    var r = (len / (n - x));
                    result += (2 * r + 1L) * (n - x);
                    var next = x - (r * (n - x));
                    if (next < 0) {
                        next = x;
                    }
                    if ((n - x) % next == 0) {
                        result += next * (2*((n - x) / next) - 1);
                    }
                    else {
                        result += next * 2;
                        result += x + 1;
                    }
                }
            sw.WriteLine(result);
        }
    }
}

internal class InputReader : IDisposable
{
    private bool isDispose;
    private readonly TextReader sr;

    public InputReader(TextReader stream)
    {
        sr = stream;
    }

    public void Dispose()
    {
        Dispose(true);
        GC.SuppressFinalize(this);
    }

    public string NextString()
    {
        var result = sr.ReadLine();
        return result;
    }

    public int NextInt32()
    {
        return Int32.Parse(NextString());
    }

    public long NextInt64()
    {
        return Int64.Parse(NextString());
    }

    public string[] NextSplitStrings()
    {
        return NextString()
            .Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries);
    }

    public T[] ReadArray<T>(Func<string, CultureInfo, T> func)
    {
        return NextSplitStrings()
            .Select(s => func(s, CultureInfo.InvariantCulture))
            .ToArray();
    }

    public T[] ReadArrayFromString<T>(Func<string, CultureInfo, T> func, string str)
    {
        return
            str.Split(new[] { ' ' }, StringSplitOptions.RemoveEmptyEntries)
                .Select(s => func(s, CultureInfo.InvariantCulture))
                .ToArray();
    }

    protected void Dispose(bool dispose)
    {
        if (!isDispose)
        {
            if (dispose)
                sr.Close();
            isDispose = true;
        }
    }

    ~InputReader()
    {
        Dispose(false);
    }
}