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;
using System.Threading.Tasks;

class _C
{
	void _()
	{
		var _n = _Ns();
		var N = _n[0];
		var X = _n[1];

		int sum = N-X;
		sum += (X)*3;
		sum += (N-2*X)*3;
		Console.WriteLine(sum);			

	}

	static void Main(string[] args)
  {
    new _C()._();
  }

  #region

  string _S()
  {
    return Console.ReadLine();
  }

  string[] _Ss()
  {
    return Console.ReadLine().Split();
  }

  int[] _N(int n)
  {
    var x = new int[n];
    for (var i = 0; i < n; i++)
    {
      x[i] = int.Parse(Console.ReadLine());
    }
    return x;
  }

  int[] _Ns()
  {
    var ss = Console.ReadLine().Split();

    var x = new int[ss.Length];
    for (var i = 0; i < ss.Length; i++)
      x[i] = int.Parse(ss[i]);

    return x;
  }
  #endregion
}