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 9.2.1) (judge verdict: Accepted)

#include<cstdio>
#include<cstring>
#include<string>
#include<iostream>
#include<cmath>
#include<algorithm>
#include<queue>
#include<map>
#include<ctime>

using namespace std;

template <typename T>

inline T read()
{
	T x=0,f=1;char c=getchar();
	while(!isdigit(c))
	{if(c=='-') f=-f;c=getchar();}
	while(isdigit(c))
	{x=(x<<3)+(x<<1)+(c-48);c=getchar();}
	return x*f;
}

#define lint long long int
#define ulint unsigned lint
#define readint read<int>()
#define readlint read<lint>()

const int inf=1e9+1e7;

lint ans=0,x,n;

lint Eclid(lint N,lint X)
{
	if(!(N%X)) return (N/X)*X*2-X;
	else return Eclid(X,N%X)+(N/X)*X*2;
}

int main(void)
{
	// freopen("testdata.in","r",stdin);
	// freopen("testdata.out","w",stdout);
	scanf("%lld%lld",&n,&x);
	ans=n+Eclid(x,n-x);
	printf("%lld\n",ans);
	return 0;
}