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.Collections.Generic;
using System.Diagnostics;
using System.IO;

internal class Program {
    static void Main() => CustomMain();

    static void Solve() {
        long n, x;
        ReadMulti(out n, out x);

        // 2辺目までは確定
        long ans = n;

        var div = (n - x) / x;
        var m = (n - x) % x;
        if (m == 0) {
            ans += (2 * div - 1) * x;
        } else {
            ans += 2 * div * x;
            ans += x + m;
        }

        WriteAnswer(ans);
    }


    static void CustomMain() {
#if DEBUG
        // ファイルからテストケースを読み込む
        ChangeStdIn();
        // 時間計測
        var stopwatch = new Stopwatch();
        stopwatch.Start();
#endif
        // 出力高速化
        var streamWriter = new StreamWriter(Console.OpenStandardOutput()) {AutoFlush = false};
        Console.SetOut(streamWriter);
        // 回答
        Solve();
#if DEBUG
        stopwatch.Stop();
        Console.WriteLine(stopwatch.Elapsed);
#endif
        Console.Out.Flush();
    }

    static string ReadString() => Console.ReadLine().Trim();
    static int ReadInt() => int.Parse(ReadString());
    static long ReadLong() => long.Parse(ReadString());
    static float ReadFloat() => float.Parse(ReadString());
    static double ReadDouble => double.Parse(ReadString());

    static string[] ReadStringArray() => ReadString().Split(' ');
    static int[] ReadIntArray() => Array.ConvertAll(ReadString().Split(' '), int.Parse);
    static long[] ReadLongArray() => Array.ConvertAll(ReadString().Split(' '), long.Parse);
    static float[] ReadFloatArray() => Array.ConvertAll(ReadString().Split(' '), float.Parse);
    static double[] ReadDoubleArray() => Array.ConvertAll(ReadString().Split(' '), double.Parse);

    static T TypeConversion<T>(string s) {
        if (typeof(T) == typeof(int)) {
            return (T) Convert.ChangeType(int.Parse(s), typeof(T));
        } else if (typeof(T) == typeof(long)) {
            return (T) Convert.ChangeType(long.Parse(s), typeof(T));
        } else if (typeof(T) == typeof(double)) {
            return (T) Convert.ChangeType(double.Parse(s), typeof(T));
        } else {
            return (T) Convert.ChangeType(s, typeof(T));
        }
    }

    static void ReadMulti<T, U>(out T a, out U b) {
        var str = ReadStringArray();
        a = TypeConversion<T>(str[0]);
        b = TypeConversion<U>(str[1]);
    }

    static void ReadMulti<T, U, V>(out T a, out U b, out V c) {
        var str = ReadStringArray();
        a = TypeConversion<T>(str[0]);
        b = TypeConversion<U>(str[1]);
        c = TypeConversion<V>(str[2]);
    }

    static void WriteAnswer(object ans) => Console.WriteLine(ans);

    static bool IsOdd(long num) {
        return (num & 1) == 1;
    }

    static bool IsEven(long num) {
        return (num & 1) == 0;
    }

    static long GCD(long a, long b) {
        return b != 0 ? GCD(b, a % b) : a;
    }


    static void ChangeStdIn() {
        var path = "./../../TestCase.txt";
        var exStdIn = new System.IO.StreamReader(path);
        Console.SetIn(exStdIn);
    }
}