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
/*
 * 高橋君は 1 辺の長さが N の 3 枚の鏡を正三角形状に組み合わせました。 三角形の頂点をそれぞれ a,b,c とします。
 * 
 * 高橋君は、辺 ab 上の頂点 a から X の点から、辺 bc と平行に不思議な光を発射しました。
 * 不思議な光は、普通の光と同じように真っすぐ進み、鏡に当たると反射するのですが、不思議な光がすでに通った点に当たったときにも反射をします。
 * 例えば、N=5,X=2 のとき、不思議な光の軌跡は図の黄色い矢印のようになります。
 * 
 * このように不思議な光を発射した時、不思議な光は必ず発射した点に戻ってくることが証明できます。 このとき、光の軌跡の長さが全体でいくらになるかを求めて下さい。
 */

import java.util.*;
	public class Main{
        public static void main(String[] args){
            Scanner sc = new Scanner(System.in);
            //入力
            long n = Long.parseLong(sc.next());
            long x = Long.parseLong(sc.next());
            long ret = n;
            
            n -= x;
            
            while(n%x != 0 && x%n != 0){
            	if(n>x){
            		ret += 2 * x * (n/x);
            		n -= x * (n/x);
            	}else{
            		ret += 2 * n * (x/n);
            		x -= n * (x/n);
            	}
            }
            
            //出力
            System.out.println(ret + Math.max(n, x) * 2 - Math.min(n,  x));
            sc.close();
        }
    }
	