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>
#include <ext/pb_ds/priority_queue.hpp>
#define priority_queue __gnu_pbds::priority_queue
typedef long long LL;
typedef long double LD;
typedef unsigned long long ul;
#define ri register int
#define pb push_back
#define fi first
#define se second
#define mid ((l + r) >> 1)
#define ls (i << 1)
#define rs (i << 1 | 1)
#define enum(i, j, k) for(int i = j; i <= k; i ++)
#define FO(x) { freopen(#x".in", "r", stdin); freopen(#x".out", "w", stdout); }
using namespace std;
typedef pair<int, int> pii;
typedef pair<LL, LL> pll;
typedef pair<int, LL> pil;
typedef pair<LL, int> pli;
typedef vector<int> vi;
#define ae(x) for(node *p = h[x]; p; p = p->nxt)
#define G \
	struct node { int v; node *nxt; } e[maxm], *h[maxn]; int z;\
	void adde(int u, int v) { e[++z].v = v; e[z].nxt = h[u]; h[u] = &e[z]; }\
	void addrev(int u, int v) { adde(u, v); adde(v, u); }
#define W \
	struct node { int v, w; node *nxt; } e[maxm], *h[maxn]; int z;\
	void adde(int u, int v, int w) { e[++z].v = v; e[z].w = w; e[z].nxt = h[u]; h[u] = &e[z]; }\
	void addrev(int u, int v, int w) { adde(u, v, w); adde(v, u, w); }
inline int _() // ret >= 0
{
	int ret = 0; char ch = getchar();
	while(ch < '0' || ch > '9') ch = getchar();
	do { ret = ret * 10 + ch - '0'; ch = getchar(); } while('0' <= ch && ch <= '9');
	return ret;
}
inline void _(int x) // x >= 0
{
	if(x < 10) { putchar(x + '0'); return ; }
	_(x / 10); putchar(x % 10 + '0');
}
void What_are_you_doing_at_the_end_of_the_world_Are_you_busy_Can_you_save_us()
{
	ios::sync_with_stdio(false); cin.tie(0); cout.tie(0);
	cout << fixed << setprecision(16);
}
/* Default Code Ends Here. */



int main()
{
	What_are_you_doing_at_the_end_of_the_world_Are_you_busy_Can_you_save_us();
	
	LL n, t;
	cin >> n >> t;
	cout << 3 * (n - 1) << endl;
	return 0;
}