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

namespace AGC001
{
    public class B
    {
        private void Run()
        {
            var input = Console.ReadLine().Trim().Split();
            var n = long.Parse(input[0]);
            var initial = long.Parse(input[1]);

            // (x,y) => 右(x+1,y), 左(x-1,y), 左下(x,y+1), 右上(x,y-1), 右下(x+1,y+1), 左上(x-1,y-1)
            // 右に進む→左下に進む、の後の位置
            long result = n;
            long x = initial;
            long y = n - initial;   // ab間のXを0とする
            long maxX = x;
            long maxY = y;

            while (true)
            {
                if (x == 0 && y == 0) { break; }
                if (y < maxX) { goto Foo; }
                // 左上に進む
                result += maxX;
                x -= maxX;
                y -= maxX;
                maxY = y;
                if (x == 0 && y == 0) { break; }
                // 右に進む→左上に進む、を繰り返えす (次にやろうとするとx=0には戻ってくれなくなる、までやる)
                result += (y / maxX) * 2;
                y %= maxX;
                maxY = y;
                if (x == 0 && y == 0) { break; }
                // 右に進む
                x = maxX;
                result += maxX;

                Foo:
                if (x == 0 && y == 0) { break; }
                // 左上に進む→左下に進む、を繰り返す(次にやろうとするとy=maxYには戻ってこれなくなる、までやる)
                long bar = (x - 1) / maxY;
                result += maxY * bar * 2;
                x -= maxY * bar;
                maxX = x;
            }

            Console.WriteLine(result);
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new B().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}