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;
#define int long long
#define fo(a,b) for(int a=0;a<b;a++)
 int wari(int a,int b) {
   if(a%b==0)
     return a/b;
   else
     return a/b+1;
 }
 int keta(int a){
  double b=a;
  b=log10(b);
  int c=b;
  return c+1;
 }
 int souwa(int a){
  return a*(a+1)/2;
 }
 int lcm(int a,int b){
  int d=a,e=b,f;
  if(a<b)
    swap(a,b);
  int c,m=1;
  while(m){
    c=a%b;
    if(c==0){
       f=b;
      m--;
    }
    else{
      a=b;
      b=c;
 }
  }
  return d*e/f;
    }
    signed main(){
  int a,b;
  cin>>a>>b;
  cout<<3*a<<endl;
}