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;
using System.Collections.Generic;
using System.Collections.Specialized;
using System.Text;
using System.Text.RegularExpressions;
using System.Linq;
using System.IO;

class Program
{ 
    static void Main(string[]args)
    {
        Magatro m = new Magatro();
        m.Scan();
        m.Solve();
    }
}

public class Scanner
{
    private StreamReader Sr;
    private string[] S;
    private int Index;

    private const char Separator=' ';

    public Scanner()
    {
        Index = 0;
        S = new string[0];
        Sr = new StreamReader(Console.OpenStandardInput());
    }

    private string[] Line()
    {
        return Sr.ReadLine().Split(Separator);
    }

    public string Next()
    {
        string result;
        if (Index >= S.Length)
        {
            S = Line();
            Index = 0;
        }
        result = S[Index];
        Index++;
        return result;
    }
    public int NextInt()
    {
        return int.Parse(Next());
    }
    public double NextDouble()
    {
        return double.Parse(Next());
    }
    public long NextLong()
    {
        return long.Parse(Next());
    }
    public string[] StringArray(int index = 0)
    {
        Next();
        Index = S.Length;
        return S.Skip(index).ToArray();
    }
    public int[] IntArray(int index = 0)
    {
        return StringArray(index).Select(int.Parse).ToArray();
    }
    public long[]LongArray(int index = 0)
    {
        return StringArray(index).Select(long.Parse).ToArray();
    }

    public bool ScanToEnd(ref string s)
    {
        if (Sr.EndOfStream)
        {
            return false;
        }
        else
        {
            s = Sr.ReadLine();
            return true;
        }
    }
}

public class Magatro
{
    private long N, X;
    public void Scan()
    {
        Scanner sc = new Scanner();
        N = sc.NextLong();
        X = sc.NextLong();
    }

    public void Solve()
    {
        Console.WriteLine(3 * (N-gcd(N, X)));
    }
    private long gcd(long n,long x)
    {
        long r = n % x;
        while (r > 0)
        {
            n = x;
            x = r;
            r = n % x;
        }
        return x;
    }
}