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: Accepted)

using System;

class Program
{
    static long N;
    static long X;

    static void Main(string[] args)
    {
        Console.Write(MysteriousLightEmulator());
    }

    private static string MysteriousLightEmulator()
    {
        readData();

        return LightLength().ToString();
    }

    /// <summary>
    /// データを読み込む
    /// </summary>
    private static void readData()
    {
        string[] line = Console.ReadLine().Split(' ');

        N = long.Parse(line[0]);

        X = long.Parse(line[1]);
    }

    private static long LightLength()
    {
        return forwardRay() + backRay();
    }

    private static long forwardRay()
    {
        return N;
    }

    private static long backRay()
    {
        long l = 0;
        long traiangleSize = N - X < X ? N - X : X;
        long n = N - traiangleSize;

        while (n > 0 && traiangleSize > 0)
        {
            l += goUp(ref n, traiangleSize);

            long tmp = n;
            n = traiangleSize;
            traiangleSize = tmp;
        }

        return l;
    }

    /// <summary>
    /// 
    /// </summary>
    /// <param name="n">移動距離</param>
    /// <param name="t">三角形の一辺の長さ</param>
    /// <returns></returns>
    private static long goUp(ref long n, long t)
    {
        long p = n / t;

        n = n - t * p;

        return n == 0 ? 2 * t * p - t : 2 * t * p;
    }

}