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 <queue>
#include <iostream>
#include <cmath>
#include <cstdlib>
#include <algorithm>
#include <stack>
#include <string>
#include <vector>
#include <stdlib.h>
#include <map>
#include <stdio.h>
using namespace std;

#define rep(i, n) for(int i = 0; i < (int)(n); i++)
#define FOR(i, a, b) for(int i = (a); i < (int)(b); i++)
#define MAX(a, b) ((ll)(a) > (ll)(b)) ? (ll)(a) : (ll)(b)
#define MIN(a, b) ((ll)(a) > (ll)(b)) ? (ll)(b) : (ll)(a)

typedef long long ll;
typedef unsigned long long ull;
typedef vector<ll> vint;
typedef vector<string> vstr;
typedef pair<ll, ll> pint;
unsigned long long inf = (1LL << 62);
ll mod = 1000000007;
pint dx[4] = { {1, 0}, {-1, 0}, {0, 1}, {0, -1}};

ll N, X;


ll solve(ll a, ll b) {

	if (a % b == 0) {

		return 2 * b * ((a / b) - 1) + b;

	}
	else {
		return 2 * b * ((a/b)) + solve(b, a % b);
	}

}


int main() {
	
	cin >> N >> X;

	cout << N + solve(MAX(N-X, X), MIN(N-X, X)) << endl;


	return 0;
}