#include <bits/stdc++.h>

#include "longesttrip.h"

using namespace std;

vector<int> longest_trip(int n, int d) {
    if (d == 3) {
        vector<int> ans(n);
        iota(ans.begin(), ans.end(), 0);
        return ans;
    }
    if (d == 2) {
        vector<int> ans = {0};
        vector<int> used(n);
        used[0] = 1;
        while (ans.size() < n) {
            int nxt = -1;
            for (int i = 0; i < n; ++i) {
                if (!used[i] && are_connected({ans.back()}, {i})) {
                    nxt = i;
                    used[i] = 1;
                    break;
                }
            }
            if (nxt == -1) {
                reverse(ans.begin(), ans.end());
                for (int i = 0; i < n; ++i) {
                    if (!used[i] && are_connected({ans.back()}, {i})) {
                        nxt = i;
                        used[i] = 1;
                        break;
                    }
                }
            }
            ans.push_back(nxt);
        }
        return ans;
    }
    if (d == 1) {
        vector<int> ans = {0};
        vector<int> used(n);
        used[0] = 1;
        auto try_to_add = [&]() {
            vector<int> vals;
            for (int i = 0; i < n; ++i) {
                if (!used[i]) {
                    vals.push_back(i);
                }
            }
            if (vals.empty()) {
                return false;
            }
            if (!are_connected({ans.back()}, vals)) {
                return false;
            }
            while (vals.size() > 1) {
                int m = vals.size() / 2;
                vector<int> vals1, vals2;
                for (int i = 0; i < (int)vals.size(); ++i) {
                    if (i < m) {
                        vals1.push_back(vals[i]);
                    } else {
                        vals2.push_back(vals[i]);
                    }
                }
                if (are_connected({ans.back()}, vals1)) {
                    vals = vals1;
                } else {
                    vals = vals2;
                }
            }
            used[vals[0]] = 1;
            ans.push_back(vals[0]);
            return true;
        };
        while (true) {
            if (!try_to_add()) {
                break;
            }
        }
        if (ans.size() < n) {
            reverse(ans.begin(), ans.end());
            if (try_to_add()) {
                while (true) {
                    if (!try_to_add()) {
                        break;
                    }
                }
            } else {
                vector<int> vals;
                for (int i = 0; i < n; ++i) {
                    if (!used[i]) {
                        vals.push_back(i);
                    }
                }
                assert(!vals.empty());
                vector<int> ans2 = ans;
                if (are_connected(ans2, ans)) {
                    while (ans2.size() > 1) {
                        int m = ans2.size() / 2;
                        vector<int> ans21, ans22;
                        for (int i = 0; i < (int)ans2.size(); ++i) {
                            if (i < m) {
                                ans21.push_back(ans2[i]);
                            } else {
                                ans22.push_back(ans2[i]);
                            }
                        }
                        if (are_connected(ans21, vals)) {
                            ans2 = ans21;
                        } else {
                            ans2 = ans22;
                        }
                    }
                    vector<int> ansl, ansr;
                    for (auto vl : ans) {
                        if (ansl.empty() || ansl.back() != ans2[0]) {
                            ansl.push_back(vl);
                        } else {
                            ansr.push_back(vl);
                        }
                    }
                    ans.clear();
                    for (auto vl : ansr) {
                        ans.push_back(vl);
                    }
                    for (auto vl : ansl) {
                        ans.push_back(vl);
                    }
                    if (try_to_add()) {
                        while (true) {
                            if (!try_to_add()) {
                                break;
                            }
                        }
                    }
                }
            }
        }
        if (ans.size() * 2 < n) {
            ans.clear();
            for (int i = 0; i < n; ++i) {
                if (!used[i]) {
                    ans.push_back(i);
                }
            }
        }
        return ans;
    }
}