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.Arrays;
import java.util.Scanner;
import java.util.TreeSet;

public class Main {
    Scanner sc = new Scanner(System.in);
  
    public static void main(String[] args) {
        new Main(); 
    }
  
    public Main() {
    	new B().doIt();
    }
    class B{
    	void doIt(){
    		long N = sc.nextLong();
    		long X = sc.nextLong();
    		long XX = X * 2;
    		if(N - XX < 0)X = N - X;
    		long NN = N - X;
//    		System.out.println(NN+" "+X);
    		if(X == 0){
    			X = NN;
    			NN = 0;
    		}
    		long sum = X + NN;
    		while(true){
//    			System.out.println(NN+" "+X);
    			if(NN % X == 0)break;
    			long cnt = (NN / X)*2;
    			sum = sum + cnt * X;
    			long temp = X;
    			X = NN % X;
    			NN = temp;
    		}
    		long cnt = (NN / X)*2 - 1;
    		sum = sum + cnt * X;
    		System.out.println(sum);
    	}
    }
}