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: Runtime Error)

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

class Program {
    static void Main(string[] args) {
        //入力
        string s = Console.ReadLine();
        int N = int.Parse(s.Split(' ')[0]);
        int X = int.Parse(s.Split(' ')[1]);

        //回答用変数
        int ans = N;

        //長辺と短辺を入れる用の変数
        int long_ = Math.Max(N - X, X);
        int short_ = Math.Min(N - X, X);

        //検証
        while (true) {
            //片方がゼロになったら抜け出す
            if (long_ == 0 || short_ == 0) {
                break;
            }

            //割り切れたら、奇数倍をかけて終了
            if (long_ % short_ == 0) {
                ans += ((long_ / short_) * 2 - 1) * short_;
                break;
            //割り切れなかったら、偶数倍をかけてもう一周回す
            } else {
                ans += (long_ / short_) * short_ * 2;
                //一時保管用
                int long_temp = long_;
                long_ = Math.Max(long_temp % short_, short_);
                short_ = Math.Min(long_temp % short_, short_);
            }
        }


        //出力
        Console.WriteLine(ans);
    }
}