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 JAVA):

Solution:
import java.util.ArrayDeque;
import java.util.Arrays;
import java.util.HashMap;
import java.util.LinkedHashMap;
import java.util.Map;
import java.util.Scanner;

public class Main {
    
    static int V;
    static Map<Integer, Map<Integer, Integer>> graph;
    static int[] deliver;
    static ArrayDeque<Move> path;

    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        V = Integer.parseInt(sc.next());
        int E = Integer.parseInt(sc.next());
        
        Edge[] e = new Edge[E];
        for(int i = 0; i < E; i++){
            e[i] = new Edge(Integer.parseInt(sc.next()), Integer.parseInt(sc.next()), Integer.parseInt(sc.next()));
        }
        Arrays.sort(e);
        
        graph = new HashMap<>();
        for(int i = 0; i < E; i++){
            int u = e[i].u;
            int v = e[i].v;
            int d = e[i].d;
            
            if(!graph.containsKey(u)){
                Map<Integer, Integer> edge = new LinkedHashMap<>();
                graph.put(u, edge);
            }
            graph.get(u).put(v, d);
            
            if(!graph.containsKey(v)){
                Map<Integer, Integer> edge = new LinkedHashMap<>();
                graph.put(v, edge);
            }
            graph.get(v).put(u, d);
        }
        
        int tMax = Integer.parseInt(sc.next());
        int[] info = new int[tMax];
        for(int i = 0; i < tMax; i++){
            int nNew = Integer.parseInt(sc.next());
            if(nNew == 1){
                int id = Integer.parseInt(sc.next());
                info[i] = Integer.parseInt(sc.next());
            }
        }
        
        ArrayDeque<Integer> order = new ArrayDeque<>();
        int orderNum = 0;
        deliver = new int[V+1];
        int deliverNum = 0;
        int pos = 1;
        path = new ArrayDeque<>();
        StringBuilder command = new StringBuilder();
        final int SHOP = 1;
        final int EDGE = 0;
        boolean returnToShop = false;
        
        for(int t = 0; t < tMax; t++){
            if(info[t] != 0){
                order.add(info[t]);
                orderNum++;
            }
            if(!path.isEmpty()){
                if(path.peek().cost == 1){
                    pos = path.poll().to;
                }else{
                    path.peek().cost--;
                    pos = EDGE;
                }
            }
            if(t == 9400) returnToShop = true;
            
            if(pos == SHOP){
                path.clear();
                while(!order.isEmpty()){
                    deliver[order.poll()]++;
                    deliverNum++;
                }
                orderNum = 0;
                if(deliverNum == 0){
                    command.append(-1);
                }else{
                    setPath(pos, -1);
                    command.append(path.peek().to);
                }
            }else if(pos == EDGE){
                command.append(path.peek().to);
            }else{
                if(deliver[pos] != 0){
                    deliverNum -= deliver[pos];
                    deliver[pos] = 0;
                }
                if(returnToShop){
                    path.clear();
                    setPath(pos, SHOP);
                    returnToShop = false;
                }else if(path.isEmpty()){
                    if(deliverNum == 0 || orderNum > deliverNum*8){
                        setPath(pos, SHOP);
                    }else{
                        setPath(pos, -1);
                    }
                }
                command.append(path.peek().to);
            }
            command.append(System.lineSeparator());
        }
        
        System.out.print(command);
    }
    
    static void setPath(int from, int to){
        
        int[] visitFrom = new int[V+1];
        Arrays.fill(visitFrom, -1);
        ArrayDeque<Integer> que = new ArrayDeque<>();
        visitFrom[from] = 0;
        que.add(from);
        
        while(true){
            int v = que.poll();
            if((to == -1 && deliver[v] != 0) || v == to){
                while(visitFrom[v] != 0){
                    int cost = graph.get(visitFrom[v]).get(v);
                    path.addFirst(new Move(v, cost));
                    v = visitFrom[v];
                }
                return;
            }
            
            Map<Integer, Integer> edge = graph.get(v);
            for(int node : edge.keySet()){
                if(visitFrom[node] < 0){
                    visitFrom[node] = v;
                    que.add(node);
                }
            }
        }
    }
    
    static class Edge implements Comparable<Edge>{
        int u;
        int v;
        int d;

        public Edge(int u, int v, int d) {
            this.u = u;
            this.v = v;
            this.d = d;
        }
        
        @Override
        public int compareTo(Edge e) {
            return this.d - e.d;
        }
    }
    
    static class Move {
        int to;
        int cost;

        public Move(int to, int cost) {
            this.to = to;
            this.cost = cost;
        }
    }
}