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: Wrong Answer)

/* it was worth becoming a chemist */
#include <bits/stdc++.h>

using namespace std;

typedef long long ll;
typedef double db;
typedef long double ld;
typedef unsigned int uni;
typedef unsigned long long unll;
typedef pair<int, int> pii;
typedef pair<long long, long long> pll;
typedef pair<long long, int> pli;
typedef pair<int, long long> pil;
typedef vector<int> vi;
typedef vector<long long> vll;

#define mp make_pair
#define pb push_back
#define all(x) (x).begin(), (x).end()
#define sz(x) (int)x.size()
#define NAME "puts"
#define F first
#define S second

const ll INF = 1e18;
const int inf = 1e9;
const int mod = 1e9 + 7;
const db EPS = (db) 1e-9;
const db pi = acos(-1.0);
const int MAXN = 1e6 + 5;


int n, x;

int main() {
    
    cin >> n >> x;
    cout << 3 * x + (n - x) + 3 * (x / 2);

    return 0;
}