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"
#define _CRT_SECURE_NO_WARNINGS
#define rep(i,n) for(int i = 0;i < n;i++)
#define REP(i,n,k) for(int i = n;i < k;i++)
#define P(p) cout << (p) << endl;
#define sP(p) cout << setprecision(15) << fixed << p << endl;
#define Pi pair<int,int>
#define IINF 1e9
#define LINF 1e18
#define vi vector<int>
#define mp make_pair
#define pb push_back

using namespace std;
typedef long long ll;
typedef unsigned long long ull;
int dx[] = { 0, 1,0,-1};
int dy[] = { 1, 0,-1,0};
int dx8[] = { -1,-1,-1,0,0,1,1,1};
int dy8[] = { -1,0,1,-1,1,-1,0,1};

unsigned long long sttoi(std::string str) {
	unsigned long long ret;
	std::stringstream ss; ss << str;
	ss >> ret;
	return ret;
}

ull gcd(ull a, ull b) {
	if (b > a)swap(a, b);
	if (b == 0) return a;
	return gcd(b, a%b);
}

int comb(int n, int k) {
	int ans = 1;
	for (int i = 0; i < min(k, n - k); i++) {
		ans *= n - i;
		ans /= i + 1;
	}
	return ans;
}

ll mod_pow(ll n,ll p,ll mod){	
	if (p == 0) return 1 % mod;
	if (p < 2) {
		return n % mod;
	}else {
		ll d = 2, value = (n%mod)*(n%mod)%mod;
		while (d*2 < p) { d *= 2;	value *= value;	value %= mod;}
		value %= mod;
		return ((value%mod) * (mod_pow(n, p - d, mod)%mod)) % mod;
	}
}

bool isPrime(int n) {
	if (n <= 1)return false;
	if (n == 2)return true;
	if (n % 2 == 0)return false;
	for (int i = 3; i*i <= n; i += 2) {
		if (n%i == 0)return false;
	}
	return true;
}

void solve() {
	ll n, x;
	cin >> n >> x;
	if (abs(n-x) == 1) {
		P(n*3 - x);
	}else if(n%2 == 0 && x == n/2){
		P(3*n/2)
	}
	else {
		P(n + x*4 - 1);
	}
}

int main() {
	solve();
	return 0;
}