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 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<stdio.h>

long long int g(long long int n, long long int m){
    //printf("%lld, %lld\n", n, m);
    if(n == 0 || m == 0) return 0;
    if(n > m) return 2 * m * (n / m) + g(n % m, m);
    if(n < m){
        if(m % n == 0) return m + 2 * n * (m / n) - n;
        else  return m + 2 * n * (m / n) + m % n + g(n - m % n, m % n);
    }
    return 2 * n;
}

signed main(void){
    long long int N, X;
    scanf("%lld", &N);
    scanf("%lld", &X);
    if(2 * X == N) printf("%lld\n", 3 * X);
    else if(2 * X < N) printf("%lld\n", N + X + g(N - 2 * X, X));
    else if(N % (N - X) == 0) printf("%lld\n", X + 2 * (N - X) * (X / (N - X)) - (N - X));
    else printf("%lld\n", X + 2 * (N - X) * (X / (N - X)) + X % (N - X) + g(X - X % (N - X), X % (N - X)));
    return 0;
}