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

namespace ConsoleApplication1
{
    class Program
    {
        static void Main(string[] args)
        {
            var str = Console.ReadLine().Split();
            var n = UInt64.Parse(str[0]);
            var x = UInt64.Parse(str[1]);
            Console.WriteLine(Solver.Solve(n, x));
        }
    }

    public class Solver
    {
        public static UInt64 Solve(UInt64 n, UInt64 x)
        {
            var ret = x + (n - x);
            ret += dfs(x, n - x);
            return ret;
        }

        public static UInt64 dfs(UInt64 a, UInt64 b)
        {
            if (a == 0 || b == 0) return 0;
            if (b % a == 0)
            {
                return a * 2 * (b / a - 1) + a;
            }

            var ret = (2 * a) * (b / a);
            if (a % (b % a) == 0) return ret + ((b % a) * 2) * (a / (b % a)) - b % a;

            ret += ((b % a) * 2) * (a / (b % a));
            return ret + dfs(a % (b % a), b % a);
        }
    }

}