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)

#include <bits/stdc++.h>

using namespace std;

typedef long long LL;

LL solve(LL n, LL x) {
    if (x + x == n) return x * 3;
    if (x + x < n) {
        LL ans = x + x + n;
        LL tmp = n - x - x;
        if (x % tmp == 0) return ans + ((x / tmp) * 2 - 1) * tmp;
        return ans + ((x / tmp) * 2 - 1) * tmp + solve(x + x % tmp, x % tmp) - x % tmp;
    }
    LL ans = x;
    LL tmp = x + x - n;
    if (x % tmp == 0) return ans + ((x / tmp) * 2) * tmp;
    return ans + ((x / tmp) * 2) * tmp + solve(x + x % tmp, x % tmp) - x % tmp;
}

int main() {
    LL n, x;
    cin >> n >> x;
    cout << solve(n, x);
}