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.

btriangle.png

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.

Input

The input is given from Standard Input in the following format:


N X


Output

Print the total length of the ray's trajectory.

Example

Input

5 2


Output

12
import java.io.*;
import java.util.StringTokenizer;

/**
 * Created by vikas.k on 26/12/16.
 */
public class Main {
    public static void main(String[] args){
        MyScanner sc = new MyScanner();
        out = new PrintWriter(new BufferedOutputStream(System.out));

        long n = sc.nextLong();
        long x = sc.nextLong();

        long a = x;
        long b = n-x;

        if(b > a){
            b = x;
            a = n-x;
        }
        long ans = n;
        while(b!=0){
            ans+= b*2*(a/b);
            long tmp = a%b;
            a=b; b=tmp;
        }
        ans-=a;
        out.println(ans);
        out.close();
    }

    public static PrintWriter out;

    private static class MyScanner{
        BufferedReader bufferedReader;
        StringTokenizer stringTokenizer;

        private MyScanner(){
            bufferedReader = new BufferedReader(new InputStreamReader(System.in));
        }

        private String next(){
            if(stringTokenizer == null || !stringTokenizer.hasMoreElements()){
                try {
                    stringTokenizer = new StringTokenizer(bufferedReader.readLine());
                } catch (IOException e) {
                    e.printStackTrace();
                }
            }
            return stringTokenizer.nextToken();
        }

        private int nextInt(){
            return Integer.parseInt(next());
        }
        private long nextLong() { return Long.parseLong(next()); }
        private String nextLine(){
            String ret= "";
            try {
                ret= bufferedReader.readLine();
            } catch (IOException e) {
                e.printStackTrace();
            }
            return ret;
        }
    }
}
