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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <map>
#include <sstream>
#include <set>
#include <iomanip>
#include <list>
#include <stack>
#include <queue>
#include <bitset>
#include <numeric>
#include <functional>

#include <cstdio>
#include <cmath>
#include <climits>
#include <cstring>
#include <cctype>
#include <cstdlib>


using namespace std;

#define tr(x) cout << x << endl;
#define tr2(x, y) cout << x << " " << y << endl;
#define tr3(x, y, z) cout << x << " " << y << " " << z << endl;
#define tr4(w, x, y, z) cout << w << " " << x << " " << y << " " << z << endl;
#define tr6(a, b, w, x, y, z) cout << a << " " << b << " " << w << " " << x << " " << y << " " << z << endl;

#define ll long long
#define fastIO  ios::sync_with_stdio(false); cin.tie(0);
inline int in() { int x; scanf("%d", &x); return x; }
inline ll inL() { ll x; scanf("%lld", &x); return x; }



int main(){
#ifdef __APPLE__
    const clock_t begin_time = clock();
    freopen("in.txt", "r", stdin);
    freopen("out.txt", "w", stdout);
#endif

    ll n = inL(), x = inL();
    
    cout << 3 * ( n - __gcd(n, x)) << endl;
    
#ifdef __APPLE__
    cout << endl;
    cout << "Time : ";
    cout << float( clock () - begin_time ) / CLOCKS_PER_SEC << endl;
#endif
    return 0;
}