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 (Clang 3.8.0) (judge verdict: Wrong Answer)

#include <cmath>
#include <iostream>
#include <vector>
#include <queue>
#include <map>
#include <set>
#include <algorithm>
#include <utility>
#include <iomanip>

#define int long long int
#define rep(i, n) for(int i = 0; i < (n); ++i)

using namespace std;

typedef pair<int, int> P;

const int INF = 1e15;
const int MOD = 1e9+7;

signed main(){
    int n, x;
    cin >> n >> x;
    int lMax = max(x, n-x);
    int lMin = min(x, n-x);

    cout << lMin * 3 * (lMax / lMin + 1) << endl;

    return 0;
}