Problem:
Score : 500 points

Problem Statement

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.

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.

Partial Points

300 points will be awarded for passing the test set satisfying N≦1000.

Another 200 points will be awarded for passing the test set without additional constraints.

Input

The input is given from Standard Input in the following format:

N X

Output

Print the total length of the ray's trajectory.

Sample Input 1

5 2

Sample Output 1

12

Refer to the image in the Problem Statement section.
The total length of the trajectory is 2+3+2+2+1+1+1 = 12.

Solution in C++14 (GCC 5.4.1) (judge verdict: Runtime Error)

#include <iostream>

using namespace std;

int calc(int width,int height){
  if(height > width){
    const int q = height / width;
    const int r = height % width;
    //cout << "(" << width << ", " << height << ")\n";
    if(r == 0)
      return 2 * q * width - width;
    else
      return 2 * q * width + calc(width,r);
  }else if(height < width){
    //cout << "(" << width << ", " << height << ")\n";
    const int q = width / height;
    const int r = width % height;
    if(r == 0)
      return 2 * q * height - height;
    else
      return 2 * q * height + calc(r,height);
  }else{
    return height;
  }
  /*
  if(height > width)
    return 2 * width + calc(width,height - width);
  else if(height < width)
    return 2 * height + calc(width - height,height);
  else
    return height;
  */
}

int main(int argc,char *argv[]){
  int ans=0;
  int N,X;
  cin >> N >> X;
  
  ans = calc(X,N-X);
  cout << ans + N << endl;
  
  return 0;
}