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: Accepted)

#include <bits/stdc++.h>
#define REP(i, n) for (int i = 0; i < n; i++)
#define REPS(i, x) for (int i = 1; i <= (int)(x); i++)
#define REPR(i, n) for (int i = n; i >= 0; i--)
#define FOR(i, m, n) for (int i = m; i < n; i++)
#define FORS(i, m, n) for (int i = m; i <= n; i++)
#define bit(n) (1LL << (n))
#define INF 2e9
#define MOD (1000000007)
#define EPS 1e-9
#define ALL(v) v.begin(), v.end()
using namespace std;
typedef long long ll;
typedef long long int lli;
int main() {
  cin.tie(0);
  ios::sync_with_stdio(false);
  lli N, X;
  cin >> N >> X;

  lli sM = max(N - X, X);
  lli sN = min(N - X, X);
  lli ans = N; // 5
  //(3,2)+4
  //(2,1)+3
  while (sM % sN != 0) {
    ans += 2ll * sN * (sM / sN);
    lli tmp = sN;
    sN = sM % sN;
    sM = tmp;
  }

  ans += 2ll * sN * (sM / sN) - sN;
  cout << ans << "\n";
}