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 {
	
	public long solve(long N, long X) {
		long longEdge = Math.max(X, N-X);
		long shortEdge = Math.min(X, N-X);
		
		long length = X + N - X;
		
		long times = 1;
		while (shortEdge > 0) {
			long num = longEdge / shortEdge;
			long left = longEdge - (shortEdge * num);

			length += (shortEdge * num * 2);
			longEdge = shortEdge;
			shortEdge = left;
			
			times++;
		}
		length -= longEdge;
		
		return length;
	}
	
	public static void main(String[] args) {
		Scanner in = new Scanner(System.in);
		long N = in.nextLong();
		long X = in.nextLong();
		in.close();
		
		Main main = new Main();
		long result = main.solve(N, X);
		
		System.out.println(result);
	}
}