Problem: Requirements

* All inputs are of non-negative integer value.
* T_{\text{max}} = 10000
* 200 \leq |V| \leq 400
* 1.5 |V| \leq |E| \leq 2 |V|
* 1 \leq u_{i}, v_{i} \leq |V| (1 \leq i \leq |E|)
* 1 \leq d_{u_i, v_i} \leq \lceil 4\sqrt{2|V|} \rceil (1 \leq i \leq |E|)
* The given graph has no self-loops / multiple edges and is guaranteed to be connected.
* 0 \leq N_{\text{new}} \leq 1
* 1 \leq \mathrm{new\\_id}_{i} \leq T_{\text{last}}+1 (1 \leq i \leq N_{\text{new}}). Note: If all orders are generated by the order generation rule as explained above, the total number of orders is at most T_{\text{last}}+1. Therefore, the possible range of \mathrm{new\\_id}_{i} should be from 1 to T_{\text{last}}+1.
* 2 \leq \mathrm{dst}_i \leq |V| (1 \leq i \leq N_{\text{new}})
* The order IDs \mathrm{new\\_{id}}_i are unique.

Input Format

Input is provided in the following form:


|V| |E|
u_{1} v_{1} d_{u_{1}, v_{1}}
u_{2} v_{2} d_{u_{2}, v_{2}}
:
u_{|E|} v_{|E|} d_{u_{|E|}, v_{|E|}}
T_{\text{max}}
\mathrm{info}_{0}
\mathrm{info}_{1}
:
\mathrm{info}_{T_{\text{max}}-1}


* In the first line |V| denotes the number of vertices, while |E| denotes the number of edges.
* The following |E| lines denote the edges of the graph. In particular, in the ith line u_{i} and v_{i} denote the edge connecting u_{i} and v_{i} and d_{u_{i}, v_{i}} the corresponding distance.
* The following line denotes the number of steps T_{\text{max}}.



In the following line, \mathrm{info}_t is information about the order from the customer that occurs at time t. \mathrm{info}_t is given in the form:


N_{\text{new}}
\mathrm{new\_id}_1 \mathrm{dst}_1
\mathrm{new\_id}_2 \mathrm{dst}_2
\vdots
\mathrm{new\_id}_{N_{\text{new}}} \mathrm{dst}_{N_{\text{new}}}


* N_{\text{new}} represents the number of new orders which appear at time t.
* The next N_{\text{new}} lines give the newly generated order information. The i-th order information indicates that the order ID \mathrm{new\\_{id}}_i of the new order, while \mathrm{dst}_i denotes the vertex to which the customer wishes the order to be delivered.
* Note: If N_{\text{new}}=0, there are no new lines.

Output Format

The Output expects T_{\text{max}} integers in the format specified below.


\mathrm{command}_{0}
\mathrm{command}_{1}
:
\mathrm{command}_{T_{\text{max}}-1}


In particular, \mathrm{command}_{i} shall specify the movement of the delivery car by using one of the following two options:

1) `stay`, if the car shall not move:


-1


2) `move w`, if the car shall be moved one step towards the neighboring vertex w


w


Note that in case of 2) w has to satisfy the following conditions:

* w \in V
* If the car is at vertex u: \left\\{ u, w \right\\} \in E .
* If the car is on the edge \left\\{ u, v \right\\}, w must either satisfy u = w or v = w.



* * *

Examples

Input




Output




Input

5 7
1 2 5
5 3 4
2 4 8
1 5 1
2 3 3
4 5 3
4 3 9
4
1
1 2
1
2 5
1
3 4
0


Output

2
-1
1
5

Solution (in CPP):

Solution:
#include <algorithm>
#include <chrono>
#include <iostream>
#include <memory>
#include <random>
#include <vector>
#include <cassert>
#include <cstdint>
using namespace std;

using int64 = int64_t;

struct Edge {
  int u;
  int v;
  int dist;
};

struct Order {
  int t;
  int dest;
};

struct Graph {
  Graph();

  // Given in input
  int V;
  vector<Edge> edges;

  // Computable
  vector<vector<int>> neighbors;
  vector<vector<int>> distance;
  vector<vector<int>> distance_to;
};

struct Problem {
  Problem(const Graph& g);

  // Given in input
  const Graph& graph;
  int64 t_max;
  vector<Order> orders;
};

class Solver {
  class State {
  public:
    State(const Problem& p) : problem_(p) {}

    bool moveTo(int p);
    void output() const;
    void updateOrder();

    int position() const { return position_; }
    int time() const { return answer_.size(); }
    const vector<int>& orders() const { return orders_; }

  private:
    const Problem& problem_;
    int position_ = -1;
    int64 score_ = 0;
    vector<int> orders_;
    int order_from_ = 0;
    vector<int> answer_;
  };

 public:
  explicit Solver(const Problem& p) : problem(p) {}

  void solve();
  void output() const;

 private:
  const Problem& problem;
  unique_ptr<State> answer;
};

Graph::Graph() {
  cin >> V;
  int E;
  cin >> E;

  neighbors.resize(V);
  distance.resize(V, vector<int>(V, -1));
  distance_to.resize(V, vector<int>(V, -1));

  for (int i = 0; i < V; ++i) {
    distance[i][i] = 0;
    distance_to[i][i] = -1;
  }
  for (int i = 0; i < E; ++i) {
    int u, v, d;
    cin >> u >> v >> d;
    --u;
    --v;
    edges.emplace_back(Edge{u, v, d});
    neighbors[u].push_back(v);
    neighbors[v].push_back(u);
    distance[u][v] = d;
    distance[v][u] = d;
    distance_to[u][v] = v;
    distance_to[v][u] = u;
  }

  // WF
  for (int k = 0; k < V; ++k) {
    for (int i = 0; i < V; ++i) {
      int ik = distance[i][k];
      if (ik < 0)
        continue;
      for (int j = 0; j < V; ++j) {
        int kj = distance[k][j];
        if (kj < 0)
          continue;
        int ij = distance[i][j];
        if (ij < 0 || ij > ik + kj) {
          distance[i][j] = ik + kj;
          distance_to[i][j] = distance_to[i][k];
        }
      }
    }
  }
}

Problem::Problem(const Graph& g) : graph(g) {
  cin >> t_max;
  for (int t = 0; t < t_max; ++t) {
    int N;
    cin >> N;
    for (int i = 0; i < N; ++i) {
      int id, dest;
      cin >> id >> dest;
      orders.emplace_back(Order{t, dest - 1});
    }
  }
}

void Solver::solve() {
  mt19937 prg;
  unique_ptr<State> state(new State(problem));
  int next = 0;
  while (state->moveTo(next)) {
    state->updateOrder();
    // Choose the closest destination, if have orders.
    // otherwise, back to 0
    int pos = state->position();
    next = 0;
    int closest = 1e+9;
    for (int id : state->orders()) {
      const Order& order = problem.orders[id];
      if (order.dest == pos)
        continue;
      int dist = problem.graph.distance[pos][order.dest];
      if (dist < closest) {
        closest = dist;
        next = order.dest;
      }
    }
  }
  answer = move(state);
}

void Solver::output() const {
  answer->output();
}

bool Solver::State::moveTo(int dest) {
  if (time() >= problem_.t_max)
    return false;

  int& from = position_;
  if (from < 0) {
    position_ = dest;
    return true;
  }
  if (from == dest) {
    answer_.push_back(-1);
    return true;
  }

  // Assume no orders on the way.
  while (time() < problem_.t_max && position() != dest) {
    int next = problem_.graph.distance_to[from][dest];
    int d = problem_.graph.distance[from][next];
    for (int i = 0; i < d && time() < problem_.t_max; ++i) {
      answer_.push_back(next + 1);
    }
    from = next;
  }
  return time() < problem_.t_max;
}

void Solver::State::updateOrder() {
  if (time() >= problem_.t_max)
    return;

  int p = position();
  const vector<Order>& g_orders = problem_.orders;
  if (p == 0) {
    // Check order
    while (order_from_ < static_cast<int>(g_orders.size()) &&
           g_orders[order_from_].t < time()) {
      orders_.push_back(order_from_++);
    }
  } else {
    // Deliver
    for (int i = orders_.size() - 1; i >= 0; --i) {
      const Order& order = g_orders[orders_[i]];
      if (order.dest == position()) {
        int64 dt = time() - order.t;
        score_ += problem_.t_max * problem_.t_max -  dt * dt;
        orders_.erase(orders_.begin() + i);
      }
    }
  }
}

void Solver::State::output() const {
  for (int out : answer_) {
    cout << out << "\n";
  }
}

int main() {
  unique_ptr<Graph> graph(new Graph);
  unique_ptr<Problem> problem(new Problem(*graph));
  unique_ptr<Solver> solver(new Solver(*problem));

  solver->solve();
  solver->output();

  return 0;
}