#include "longesttrip.h"

#include <cassert>
#include <cmath>
#include <cstdint>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <algorithm>
#include <bitset>
#include <complex>
#include <deque>
#include <functional>
#include <iostream>
#include <limits>
#include <map>
#include <numeric>
#include <queue>
#include <set>
#include <sstream>
#include <string>
#include <unordered_map>
#include <unordered_set>
#include <utility>
#include <vector>

using namespace std;

using Int = long long;

template <class T1, class T2> ostream &operator<<(ostream &os, const pair<T1, T2> &a) { return os << "(" << a.first << ", " << a.second << ")"; };
template <class T> ostream &operator<<(ostream &os, const vector<T> &as) { const int sz = as.size(); os << "["; for (int i = 0; i < sz; ++i) { if (i >= 256) { os << ", ..."; break; } if (i > 0) { os << ", "; } os << as[i]; } return os << "]"; }
template <class T> void pv(T a, T b) { for (T i = a; i != b; ++i) cerr << *i << " "; cerr << endl; }
template <class T> bool chmin(T &t, const T &f) { if (t > f) { t = f; return true; } return false; }
template <class T> bool chmax(T &t, const T &f) { if (t < f) { t = f; return true; } return false; }


// [0, 2^32)
unsigned xrand() {
  static unsigned x = 314159265, y = 358979323, z = 846264338, w = 327950288;
  unsigned t = x ^ x << 11; x = y; y = z; z = w; return w = w ^ w >> 19 ^ t ^ t >> 8;
}


// bool are_connected(std::vector<int> A, std::vector<int> B);

bool mem[256][256];
bool cache[256][256];
bool A(int u, int v) {
  if (u == v) return false;
  if (u > v) swap(u, v);
  bool &ret = cache[u][v];
  if (!mem[u][v]) {
    mem[u][v] = true;
    ret = are_connected({u}, {v});
  }
  return ret;
}

std::vector<int> longest_trip(int N, int D)
{
  memset(mem, 0, sizeof(mem));
  memset(cache, 0, sizeof(cache));
  
  vector<int> paths[2];
  {
    auto conn = [&]() -> void {
      reverse(paths[1].begin(), paths[1].end());
      paths[0].insert(paths[0].end(), paths[1].begin(), paths[1].end());
      paths[1].clear();
    };
    vector<int> us(N);
    for (int u = 0; u < N; ++u) {
      swap(us[xrand() % (u + 1)], us[u] = u);
    }
    paths[0] = {us[0]};
    paths[1] = {us[1]};
    for (int j = 2; j < N; ++j) {
      const int v0 = paths[0].back();
      const int v1 = paths[1].back();
      const int u = us[j];
      if (A(u, v0)) {
        paths[0].push_back(u);
      } else if (A(u, v1)) {
        paths[1].push_back(u);
      } else {
        conn();
        paths[1] = {u};
      }
// cerr<<"paths = ";pv(paths,paths+2);
    }
  }
  
  if (paths[0].size() < paths[1].size()) {
    swap(paths[0], paths[1]);
  }
  if (!are_connected(paths[0], paths[1])) {
    return paths[0];
  }
  
  int x0, x1;
  {
    int lo = 0, hi = paths[0].size();
    for (; lo + 1 < hi; ) {
      const int mid = (lo + hi) / 2;
      (are_connected(vector<int>(paths[0].begin() + lo, paths[0].begin() + mid), paths[1]) ? hi : lo) = mid;
    }
    x0 = paths[0][lo];
  }
  {
    int lo = 0, hi = paths[1].size();
    for (; lo + 1 < hi; ) {
      const int mid = (lo + hi) / 2;
      (are_connected({x0}, vector<int>(paths[1].begin() + lo, paths[1].begin() + mid)) ? hi : lo) = mid;
    }
    x1 = paths[1][lo];
  }
// cerr<<"paths = "<<paths<<", x0 = "<<x0<<", x1 = "<<x1<<endl;
  vector<set<int>> graph(N);
  auto ae = [&](int u, int v) -> void {
    graph[u].insert(v);
    graph[v].insert(u);
  };
  auto be = [&](int u, int v) -> void {
    graph[u].erase(v);
    graph[v].erase(u);
  };
  for (int j = 0; j < 2; ++j) {
    for (int k = 0; k < (int)paths[j].size() - 1; ++k) {
      ae(paths[j][k], paths[j][k + 1]);
    }
  }
  ae(x0, x1);
  for (; ; ) {
    vector<int> ls;
    for (int u = 0; u < N; ++u) if (graph[u].size() == 1) {
      ls.push_back(u);
    }
    if (ls.size() <= 1) {
      assert(false);
    } else if (ls.size() == 2) {
      vector<int> ans;
      for (int u = ls[0]; ; ) {
        ans.push_back(u);
        if (u == ls[1]) break;
        const int v = *graph[u].begin();
        be(u, v);
        u = v;
      }
      return ans;
    } else {
      for (int j0 = 0; j0 < 3; ++j0) for (int j1 = j0 + 1; j1 < 3; ++j1) {
        if (A(ls[j0], ls[j1])) {
          vector<int> us;
          for (int u = ls[j0]; graph[u].size() == 1; ) {
            us.push_back(u);
            const int v = *graph[u].begin();
            be(u, v);
            u = v;
          }
          int p = ls[j1];
          for (const int u : us) {
            ae(p, u);
            p = u;
          }
          goto found;
        }
      }
      assert(false);
     found:{}
    }
  }
}