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: Wrong Answer)

#include <bits/stdc++.h>
#define F(i,j,k) for(int i=(j);i<=(k);++i)
#define _F(i,j,k) for(int i=(j);i<(k);++i)
#define D(i,j,k) for(int i=(j);i>=(k);--i)
#define _D(i,j,k) for(int i=(j);i>(k);--i)
#define rep(it,s) for(__typeof(s.begin()) it=s.begin();it!=s.end();++it)
#define Rep(a,s) for(auto a:s)
#define PB push_back
#define MP make_pair
#define FF first
#define SS second
typedef long long ll;
typedef unsigned long long ull;
using namespace std;
template<class Type>ll quick_pow(Type x,Type y,Type Mod){
    ll res=1;
    while(y){
        if(y&1)res=res*x%Mod;
        x=x*x%Mod,y>>=1;
    }
    return res;
}
template<class Type>ll inv(Type x,Type Mod){return quick(x,Mod-2,Mod);}
namespace IO{
    template <class T>
    inline void read(T &x){
        x=0;int f=1;char ch=getchar();
        while(ch<'0'||ch>'9'){if(ch=='-')f=-1;ch=getchar();}
        while(ch<='9'&&ch>='0')x=x*10+ch-'0',ch=getchar();
        x*=f;
    }
};
using namespace IO;
ll f(ll x,ll y){
    if(y%x==0)return 2*(y/x)*x;
    else return 2*(y/x)*x+f(y%x,x);
}
int main(){
    #ifndef ONLINE_JUDGE
        freopen("in.txt","r",stdin);
        freopen("out.txt","w",stdout);
    #endif
    ll n,x;
    cin>>n>>x;
    cout<<f(x,n)<<endl;
	return 0;
}