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.IO;

#region Program
namespace Program
{
    #region Solver
    public class Solver
    {
        static IO.StreamScanner
        sc = new IO.StreamScanner(Console.OpenStandardInput());

        int N;
        int X;

        #region Solver
        public Solver()
        {
            N = sc.Integer();
            X = sc.Integer();
        }
        #endregion

        #region Solve
        public void Solve()
        {
            Console.WriteLine(N == 2 * X ? 3 * X : 4 * (N - X));
        }
        #endregion
    }
    #endregion
}
#endregion

#region Execute
class Execute
{
    public static void Main(string[] args)
    {
        new Program.Solver().Solve();
        Program.IO.Printer.Out.Flush();
    }
}
#endregion

#region Program.IO
namespace Program.IO
{
    using System.Text;
    using System.Globalization;
    using System.Linq;
    public class Printer : StreamWriter
    {
        static Printer()
        {
            Out = new Printer(Console.OpenStandardOutput())
            {
                AutoFlush = false
            };
        }
        public static Printer Out
        {
            get;
            set;
        }
        public override IFormatProvider FormatProvider
        {
            get
            {
                return CultureInfo.InvariantCulture;
            }
        }
        public Printer(System.IO.Stream stream)
            : base(stream, new UTF8Encoding(false, true))
        {
        }
        public Printer(System.IO.Stream stream, Encoding encoding)
            : base(stream, encoding)
        {
        }
        public void Write<T>(string format, T[] source)
        {
            base.Write(format, source.OfType<object>().ToArray());
        }
        public void WriteLine<T>(string format, T[] source)
        {
            base.WriteLine(format, source.OfType<object>().ToArray());
        }
    }
    public class StreamScanner
    {
        public readonly Stream str;
        private readonly byte[] buf = new byte[1024];
        private int len, ptr;
        public bool isEof = false;
        public StreamScanner(Stream stream)
        {
            str = stream;
        }
        private T[] enumerate<T>(int n, Func<T> f)
        {
            var a = new T[n];
            for (int i = 0; i < n; ++i) a[i] = f();
            return a;
        }
        public long Long()
        {
            if (isEof)
            {
                return long.MinValue;
            }
            long ret = 0;
            byte b = 0;
            var ng = false;
            do
            {
                b = read();
            }
            while (b != '-' && (b < '0' || '9' < b));
            if (b == '-')
            {
                ng = true;
                b = read();
            }
            for (; true; b = read())
            {
                if (b < '0' || '9' < b)
                {
                    return ng ? -ret : ret;
                }
                else ret = ret * 10 + b - '0';
            }
        }
        public long[] Long(int n)
        {
            return enumerate(n, Long);
        }
        public int Integer()
        {
            return (isEof) ? int.MinValue : (int)Long();
        }
        public int[] Integer(int n)
        {
            return enumerate(n, Integer);
        }
        public char[] Char(int n)
        {
            return enumerate(n, Char);
        }
        public char Char()
        {
            byte b = 0;
            do
            {
                b = read();
            }
            while ((b < 33 || 126 < b) && !isEof);
            return (char)b;
        }
        public string Scan()
        {
            var sb = new StringBuilder();
            for (var b = Char(); b >= 33 && b <= 126; b = (char)read())
            {
                sb.Append(b);
            }
            return sb.ToString();
        }
        private byte read()
        {
            if (isEof)
            {
                return 0;
            }
            if (ptr >= len)
            {
                ptr = 0;
                if ((len = str.Read(buf, 0, 1024)) <= 0)
                {
                    isEof = true;
                    return 0;
                }
            }
            return buf[ptr++];
        }
    }
}
#endregion