#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) {
        mt19937 rnd(57);
        vector<vector<int>> blocks;
        for (int i = 0; i < n; ++i) {
            blocks.push_back({i});
        }
        shuffle(blocks.begin(), blocks.end(), rnd);
        vector<int> ans = blocks.back();
        blocks.pop_back();
        auto try_to_add = [&](vector<int> vals) {
            if (vals.empty()) {
                return -1;
            }
            if (!are_connected({ans.back()}, vals)) {
                return -1;
            }
            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;
                }
            }
            return vals[0];
        };
        while (!blocks.empty()) {
            shuffle(blocks.begin(), blocks.end(), rnd);
            bool change = false;
            while (blocks.size() > 1) {
                if (are_connected({ans.back()}, {blocks.back()[0]})) {
                    change = true;
                    for (auto vl : blocks.back()) {
                        ans.push_back(vl);
                    }
                    blocks.pop_back();
                    break;
                }
                if (are_connected({ans.back()}, {blocks.rbegin()[1].back()})) {
                    change = true;
                    swap(blocks.back(), blocks.rbegin()[1]);
                    reverse(blocks.back().begin(), blocks.back().end());
                    for (auto vl : blocks.back()) {
                        ans.push_back(vl);
                    }
                    blocks.pop_back();
                    break;
                }
                for (auto vl : blocks.back()) {
                    blocks.rbegin()[1].push_back(vl);
                }
                blocks.pop_back();
            }
            if (change) {
                continue;
            }
            if (are_connected({ans.back()}, {blocks[0].back()})) {
                reverse(blocks.back().begin(), blocks.back().end());
                for (auto vl : blocks.back()) {
                    ans.push_back(vl);
                }
                blocks.pop_back();
            } else {
                int val = try_to_add(blocks[0]);
                if (val != -1) {
                    vector<int> vals1, vals2;
                    for (auto vl : blocks[0]) {
                        if (vals2.empty() && vl != val) {
                            vals1.push_back(vl);
                        } else {
                            vals2.push_back(vl);
                        }
                    }
                    for (auto vl : vals2) {
                        ans.push_back(vl);
                    }
                    for (auto vl : vals1) {
                        ans.push_back(vl);
                    }
                    blocks.pop_back();
                } else {
                    break;
                }
            }
        }
        if (!blocks.empty()) {
            reverse(ans.begin(), ans.end());
            int val = try_to_add(blocks[0]);
            if (val != -1) {
                vector<int> vals1, vals2;
                for (auto vl : blocks[0]) {
                    if (vals2.empty() && vl != val) {
                        vals1.push_back(vl);
                    } else {
                        vals2.push_back(vl);
                    }
                }
                for (auto vl : vals2) {
                    ans.push_back(vl);
                }
                for (auto vl : vals1) {
                    ans.push_back(vl);
                }
                blocks.pop_back();
            } else {
                vector<int> ans2 = ans;
                if (are_connected(ans2, blocks[0])) {
                    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, blocks[0])) {
                            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);
                    }
                    int val = try_to_add(blocks[0]);
                    if (val != -1) {
                        vector<int> vals1, vals2;
                        for (auto vl : blocks[0]) {
                            if (vals2.empty() && vl != val) {
                                vals1.push_back(vl);
                            } else {
                                vals2.push_back(vl);
                            }
                        }
                        for (auto vl : vals2) {
                            ans.push_back(vl);
                        }
                        for (auto vl : vals1) {
                            ans.push_back(vl);
                        }
                        blocks.pop_back();
                    }
                }
            }
        }
        if (!blocks.empty() && blocks[0].size() > ans.size()) {
            ans = blocks[0];
        }
        return ans;
    }
}