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: Accepted)

#include <bits/stdc++.h>
#define res register ll
#define ll long long
using namespace std;
ll n,x,ans;
inline ll read()
{
  ll X=0,w=0;
  char ch=0;
  while(!isdigit(ch))
  {
    w|=ch=='-';
    ch=getchar();
  }
  while(isdigit(ch)) X=(X<<3)+(X<<1)+(ch^48),ch=getchar();
  return w?-X:X;
}
inline void dfs(res l,res s)
{
  if(l%s==0)
  {
    ans+=(l<<1)-s;
    return;
  }
  ans+=l/s*s*2;
  dfs(s,l%s);
}
int main()
{
  n=read(),x=read();
  ans=n;
  if(x>=n-x)
    dfs(x,n-x);
  else
    dfs(n-x,x);
  printf("%lld\n",ans);
  return 0;
}