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.Linq;//リストの使用
using System.Collections.Generic;
class Program
{
	static void Main()
	{
	string[] input = Console.ReadLine().Split(' ');//Splitで区切り文字を指定して複数個受け取る。
	long n = long.Parse(input[0]);
	long x = long.Parse(input[1]);
  long answer = 0;
  long a = 0;
  long b = 0;

  answer += n;
  a = Math.Min(x,n-x);
  b = Math.Max(x,n-x);

    while(true)
    {
      //Console.WriteLine(a + " " + b + " " + answer);
      answer += 2 * a * (b/a);
      if(b % a == 0) 
      {
        answer -= a;
        break;
      }else
      {
      b = b % a;
      long temp = a;
      a = b;
      b = temp;
      }
    }
  
	Console.WriteLine(answer);//WriteLineをWriteとすると、改行なしで出力。
	}
}