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auto res = bellmanford(g, s, e);

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struct bellmanford_return {
  vector<int> path, distances;
  bool hascycle;
};
bellmanford_return bellmanford(DirectedGraph &_g,int s, int e) {
  vector<int> cnt(_g.g.size()), dist(_g.g.size(), INF), path, p(_g.g.size(), -1);
  vector<bool> inque(_g.g.size());
  queue<int> q;
  dist[s] = 0;
  q.push(s);
  inque[s] = true;
  while (!q.empty()) {
    const int from = q.front();
    q.pop();
    inque[from] = false;
    for (const auto &edge : g[from]) {
      const int d = (dist[from] + edge.cost);
      if (d < dist[edge.to]) {
        dist[edge.to] = d;
        p[edge.to] = from;
        if (!inque[edge.to]) {
          q.push(edge.to);
          inque[edge.to] = true;
          ++cnt[edge.to];
          if ((int)g.size() < cnt[edge.to])
            return {vector<int>(), vector<int>(), true};
        }
      }
    }
  }
  if (dist[e] != INF) {
    for (int i = e; i != -1; i = p[i])
      path.push_back(i);
    reverse(path.begin(), path.end());
  }
  return {path, dist, false};
}