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 JavaScript (node.js v5.12) (judge verdict: Runtime Error)

function Main(input) {

  let inputs = input.split('\n');

  let N, X;
  [N, X] = inputs[0].split(' ').map((e) => Number(e));

  let ans = N;
  let a = X, b = N - X;
  while (a % b != 0) {
    ans += 2 * Math.floor(a / b) * b;
    [a, b] = [b, a % b];
  }
  ans += 2 * a - b;

  console.log('%d', ans);

}

Main(require('fs').readFileSync('/dev/stdin', 'utf8'));

function debug() {

  let input = document.getElementById('input').value;
  Main(input);

}