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.Scanner;

public class Main {

    private static long calcRec(long shorter, long longer) {
        long leftover = longer % shorter;
        long len = (longer / shorter) * 2 * shorter;

        if (leftover == 0) {
            return len - shorter;

        } else {
            return len + calcRec(leftover, shorter);
        }
    }

    private static long calcLen(long n, long x) {

        long len = n; // first two bounces == x + (n - x)

        if (2 * x == n) {
            return len + x;

        } else if (2 * x < n) {
            return len + calcRec(x, n - x);

        } else {
            return len + calcRec(n - x, x);
        }

    }

    public static void main(String[] args) {
        Scanner sc = new Scanner(System.in);
        long n = sc.nextLong();
        long x = sc.nextLong();

        System.out.println(calcLen(n, x));
    }
}
