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;
using System.Collections.Generic;
using System.Text;

namespace AtTest.AGC_Challenge
{
    class _001_B
    {
        static void Main(string[] args)
        {
            Method(args);
            Console.ReadLine();
        }

        static void Method(string[] args)
        {
            long[] nx = ReadLongs();
            long n = nx[0];
            long x = nx[1];
            Console.WriteLine(Length(n, x));
        }

        static long Length(long n, long x)
        {
            if (x <= n - x)
            {
                long cnt = (n - x) / x;
                if ((n - x) % x == 0)
                {
                    return x * 3 * cnt;
                }
                else
                {
                    long margin = (n - x) % x;
                    return x * 3 * cnt + Length(margin + x, x);
                }
            }
            else
            {

                long cnt = x / (n - x);
                if (x % (n - x) == 0)
                {
                    return (n - x) * 3 * cnt;
                }
                else
                {
                    long nextX = x % (n - x);
                    return (n - x) * 3 * cnt + Length(n - x + nextX, nextX);
                }
            }
        }

        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }
    }
}