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.*;
import java.util.*;
public class Main {
  public static void main(String[] args) throws Exception {
    String line = null;
    long sum = 0L;
    BufferedReader br = new BufferedReader(new InputStreamReader(System.in));
    line = br.readLine();
    String data[] = line.split(" ");
    long n = Long.parseLong(data[0]);
    long x = Long.parseLong(data[1]);
    //System.out.println("N=" + n + ",X=" + x);
    long a = 0L; // 短辺の長さ
    long b = 0L; // 長辺の長さ
    long c = 0L; // 正三角形の数
    long d = 0L; // 長辺の残り
    long cnt = 0L;

    while (true) {
      if (cnt == 0L) {
        if (x >= (n - x)) {
          a = n - x;
          b = x;
        } else {
          a = x;
          b = n - x;
        }
      } else {
        b = a;
        a = d;
      }
      c = b / a;
      d = b % a;
      sum = sum + (c * 3L * a);
      //System.out.println("a=" + a + ",b=" + b + ",c=" + c + ",d=" + d + ",sum=" + sum);
      if (d == 0L) {
        break;
      }
      cnt = cnt + 1L;
    }
    System.out.println(sum);
  }
}