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: Time Limit Exceeded)

using System;
//using System.Collections.Generic;
//using System.Linq;
class Program
{
    static void Main()
    {
        string[] s = Console.ReadLine().Split();
        long n, x;
        n = long.Parse(s[0]);
        x = long.Parse(s[1]);
        C.WriteLine(f(n, x));
    }
    static long f(long n, long x)
    {
        if (x == 0)
            return 0;
        if (x <= (double)n / 2)
            return f(n - x, n - 2 * x) + 3 * x;
        if (x > (double)n / 2)
            return f(x, 2 * x - n) + 3 * n - 3 * x;
        return 0;
    }
}
//以下標準出力用のクラス
static class C
{
    [System.Runtime.InteropServices.DllImport("msvcrt.dll")]
    private static extern void printf(string s);
    public static void Write(string s) { printf(s); }
    public static void Write(char c) { printf(c.ToString()); }
    public static void Write(long n) { printf(n.ToString()); }
    public static void Write(int n) { printf(n.ToString()); }
    public static void Write(double d) { printf(d.ToString()); }
    public static void WriteLine() { printf("\n"); }
    public static void WriteLine(string s) { printf(s + "\n"); }
    public static void WriteLine(char c) { WriteLine(c.ToString()); }
    public static void WriteLine(long n) { WriteLine(n.ToString()); }
    public static void WriteLine(int n) { WriteLine(n.ToString()); }
    public static void WriteLine(double d) { WriteLine(d.ToString()); }
    public static void WriteLines(string[] s) { foreach (var i in s) WriteLine(i); }
    public static void WriteLines(char[] c) { foreach (var i in c) WriteLine(i); }
    public static void WriteLines(long[] c) { foreach (var i in c) WriteLine(i); }
    public static void WriteLines(int[] c) { foreach (var i in c) WriteLine(i); }
    public static void WriteLines(double[] d) { foreach (var i in d) WriteLine(i); }
}