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.util.*;
import java.io.*;
import java.math.*;


import static java.lang.Math.*;
import static java.util.Arrays.*;
import static java.util.Collections.*;


public class Main{ 


    static long mod=1000000007;
    //  static int dx[]={1,-1,0,0};
    //  static int dy[]={0,0,1,-1};
    // static int dx[]={1,-1,0,0,1,1,-1,-1};
    // static int dy[]={0,0,1,-1,1,-1,1,-1}; 

public  static void main(String[] args)   throws Exception, IOException{

    
    Reader sc = new Reader(System.in);
    PrintWriter out=new PrintWriter(System.out);

//  int n=sc.nextInt();  
    long n=sc.nextLong();
    long x=sc.nextLong();

    out.println(3*(n-gcd(n,x)));
    out.flush();
}

 static long gcd(long a, long b){
                 if(min(a,b) == 0) return max(a,b);
                 return gcd(max(a, b) % min(a,b), min(a,b));
         }

static void db(Object... os){

    System.err.println(Arrays.deepToString(os));

}

static boolean validpos(int x,int y,int r, int c){
    
    return x<r && 0<=x && y<c && 0<=y;
    
}
 
static boolean bit(long x,int k){
    // weather k-th bit (from right) be one or zero
    return  ( 0 < ( (x>>k) & 1 )  )  ? true:false;
}

}







class Reader
{ 
    private BufferedReader x;
    private StringTokenizer st;
    
    public Reader(InputStream in)
    {
        x = new BufferedReader(new InputStreamReader(in));
        st = null;
    }
    public String nextString() throws IOException
    {
        while( st==null || !st.hasMoreTokens() )
            st = new StringTokenizer(x.readLine());
        return st.nextToken();
    }
    public int nextInt() throws IOException
    {
        return Integer.parseInt(nextString());
    }
    public long nextLong() throws IOException
    {
        return Long.parseLong(nextString());
    }
    public double nextDouble() throws IOException
    {
        return Double.parseDouble(nextString());
    }
}

