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: Runtime Error)

#include <bits/stdc++.h>
using namespace std;
#define MOD 1000000007
//#define MOD 998244353
#define INF 1145141919810893364
typedef pair<int,int> PP;
typedef long long ll;
#define int ll
#define setdouble setprecision
#define REP(i,n) for(int i=0;i<(n);++i)
#define RREP(i,n) for(int i=(n)-1;i>=0;--i)
#define GOODBYE cout << -1 << endl;return 0
#define Endl endl

signed main(void){
    int N,X;
    cin >> N >> X;
    int Ans=N;
    
    int a=N-X,b=X;
    if(a>b)swap(a,b);
    while(1){
        Ans+=2*a*(b/a);
        b=b%a;
        if(a>b)swap(a,b);
        if(a==1){
            Ans+=2*b-1;
            break;
        }
        
    }
    cout << Ans << endl;
    return 0;
}