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<bits/stdc++.h>
using namespace std;
#define int long

signed main(){
  int n,x;
  cin>>n>>x;
  int a=x,b=n-x,c=n;
  int res=x;
  if(a==b)return cout<<x*3,0;
  while(true){
    if(a>b){
      int t=a/b;
      if(t>1)--t;
      res+=t*b*2;
      cerr<<t<<"\n";
      a-=t*b;
      c-=t*b;
      cerr<<"a,c:"<<a<<","<<c<<"\n";
    }
    else if(a<b){
      res+=c;
      int an,bn,cn;
      an=2*b-c;
      bn=c-b;
      cn=b;
      a=an;
      b=bn;
      c=cn;
    }
    else{
      res+=b*2;
      return cout<<res,0;
    }
  }
  
}