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

class A {
    static int N, X;
    static void Main() {
        string[] a = Console.ReadLine().Split(' ');
        N = int.Parse(a[0]);
        X = int.Parse(a[1]);
        if (N >= X * 2) {

            int cnt = 0;
            int q = N - X;
            int e = X;
            while (true) {
                if (q == 0) {
                    break;
                }
                cnt += 3 * e;
                int r = q;
                q = e;
                e = r - e;
            }
            Console.WriteLine(cnt);
        }
        else {
            int cnt = X;
            int q = N - X;
            int e = N;
            while (true) {
                cnt += (e / q) * q;
                int r = q;
                q = e % q;
                e = r;
                if (q == 0) {
                    break;
                }
            }
            Console.WriteLine(cnt);
        }
    }
}