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.BufferedReader;
import java.io.InputStreamReader;

public class Main {
    public static void main(String[] args) throws Exception {
        // Your code here!
        BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
        String line = br.readLine();
        String[] num = line.split(" ");
        long n = Long.parseLong(num[0]);
        long x = Long.parseLong(num[1]);
        long result = n; //真横にx、反射してn-xまでは確定なので、合計値のnを初期値とする。
        long divisor;
        long divided;
        if(n-x > x){
            divided = n-x;
            divisor = x;
        } else {
            divided = x;
            divisor = n-x;
        }
        long a;
        while(true){
            result = result + 2 * divisor * (divided / divisor);
            if(divided % divisor == 0){
                result = result - divisor;
                break;
            }
            a = divided;
            divided = divisor;
            divisor = a % divisor;
        }
        System.out.println(result);
    }
}
