// #pragma GCC optimize("O3,Ofast,unroll-loops")
// #pragma GCC target("avx2,bmi,bmi2,lzcnt,popcnt")
#include <bits/stdc++.h>
#include "fun.h"
using namespace std;
#define lli long long int
#define MP make_pair
#define pb push_back
#define REP(i,n) for(int i = 0; (i) < (n); (i)++)
#define all(x) x.begin(), x.end()
#define rall(x) x.rbegin(), x.rend()
void fastio() {
ios_base::sync_with_stdio(false);
cin.tie(NULL);
}
const double EPS = 0.00001;
const int INF = 1e9+500;
const int ALPH = 26;
const int LGN = 25;
constexpr int MOD = 1e9+7;
int n;
int centro = 0;
vector<int> roots;
vector<vector<array<int,2> > > subs;
array<int,2> isMerge() {
if(subs.size() <= 2) return {-1, -1};
array<array<int,2> ,3> s;
REP(i, 3) {
s[i] = {(int)subs[i].size(), i};
}
sort(all(s));
if(s[0][0] >= s[1][0] + s[2][0]) {
return {s[1][1], s[2][1]};
}
return {-1, -1};
}
std::vector<int> createFunTour(int N, int Q) {
n = N;
int mn = INF;
for(int i = 1; i<n; i++) {
int tmp = attractionsBehind(0, i);
if(tmp * 2 > N) {
if(mn > tmp) {
mn = tmp;
centro = i;
}
}
}
// cout << "centro:" << centro << endl;
for(int i = 0; i < n; i++) {
if(i == centro) continue;
if(hoursRequired(centro, i) == 1) {
roots.pb(i);
}
}
subs.assign(roots.size(), vector<array<int, 2> >());
for(int i = 0; i < n; i++) {
if(i == centro) continue;
int d1, d2;
d1 = hoursRequired(roots[0], i);
if(roots.size() > 1) {
d2 = hoursRequired(roots[1], i);
if(d1 == d2) {
subs[2].pb({d1 - 1, i});
}
else if(d1 > d2) {
subs[1].pb({d2 + 1, i});
}
else {
subs[0].pb({d1 + 1, i});
}
}
else {
subs[0].pb({d1 + 1, i});
continue;
}
}
for(int i = 0; i < roots.size(); i++) {
sort(all(subs[i]));
}
vector<int> ret;
int curp = 0, last = 0;
int lh = 0;
// for(auto &c : subs) {
// for(auto &i : c) {
// cout << i[0] << " " << i[1] << "\n";
// }
// cout << "new c\n";
// }
for(int z = 0; z < n - 1; z++) {
curp = -1;
if(z != 0 && subs.size() > 2) {
bool f1 = 1;
REP(i, 3) {
if(i == last) continue;
if(subs[i].back()[0] > lh) {
f1 = 0;
}
}
auto tmp = isMerge();
if(tmp[0] > tmp[1]) swap(tmp[0], tmp[1]);
if(f1 && tmp[0] != -1) {
// cout << "merged" << "\n";
vector<array<int,2> > arr(subs[tmp[0]].size() + subs[tmp[1]].size());
merge(all(subs[tmp[0]]), all(subs[tmp[1]]), arr.begin());
swap(subs[tmp[0]], arr);
subs.pop_back();
}
}
for(int i = 0; i < subs.size(); i++) {
if(i == last) continue;
if(curp == -1 || subs[curp].back()[0] < subs[i].back()[0]) {
curp = i;
}
else if(subs[curp].back()[0] == subs[i].back()[0] && subs[curp].size() < subs[i].size()) {
curp = i;
}
}
ret.pb(subs[curp].back()[1]);
lh = subs[curp].back()[0];
subs[curp].pop_back();
if(subs[curp].size() == 0) {
swap(subs[curp], subs[subs.size() - 1]);
subs.pop_back();
curp = -1;
}
last = curp;
// cout << ret.back() << endl;
}
ret.pb(centro);
// for(auto c : ret) {
// cout << c << " ";
// }
// cout << endl;
return ret;
}
