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.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;
import java.util.Scanner;

public class Main {
    
    static int V;
    static int[] deliver;
    static ArrayDeque<Move> path;
    static int[][] dist;
    static int[][] next;
    static Map<Integer, List<Node>> nodeList;
    static int orderNum;
    static int deliverNum;
    static final int SHOP = 1;
    static final int EDGE = 0;
    
    public static void main(String[] args) {
        
        Scanner sc = new Scanner(System.in);
        
        V = Integer.parseInt(sc.next());
        int E = Integer.parseInt(sc.next());
        
        dist = new int[V+1][V+1];
        final int INF = Integer.MAX_VALUE / 10;
        for(int i = 1; i <= V; i++){
            Arrays.fill(dist[i], INF);
        }
        
        for(int i = 0; i < E; i++){
            int u = Integer.parseInt(sc.next());
            int v = Integer.parseInt(sc.next());
            int d = Integer.parseInt(sc.next());
            dist[u][v] = d;
            dist[v][u] = d;
        }
        next = new int[V+1][V+1];
        for(int i = 1; i <= V; i++){
            for(int j = 1; j <= V; j++){
                next[i][j] = j;
            }
        }
        for(int k = 1; k <= V; k++){
            for(int i = 1; i <= V; i++){
                for(int j = 1; j <= V; j++){
                    if(dist[i][k] + dist[k][j] < dist[i][j]){
                        dist[i][j] = dist[i][k] + dist[k][j];
                        next[i][j] = next[i][k];
                    }
                }
            }
        }
        
        nodeList = new HashMap<>();
        for(int i = 1; i <= V; i++){
            List<Node> list = new ArrayList<>();
            for(int j = 1; j <= V; j++){
                if(i != j) list.add(new Node(j, dist[i][j]));
            }
            Collections.sort(list);
            nodeList.put(i, list);
        }
        
        int tMax = Integer.parseInt(sc.next());
        int[] info = new int[tMax];
        for(int t = 0; t < tMax; t++){
            int nNew = Integer.parseInt(sc.next());
            if(nNew == 1){
                int id = Integer.parseInt(sc.next());
                info[t] = Integer.parseInt(sc.next());
            }
        }
        
        long maxScore = 0;
        StringBuilder bestCommand = new StringBuilder();
        
        for(int a = 1; a < 300; a++){
            for(int b = 0; b < 9; b++){
                for(int c = 0; c < 9; c++){
                    ArrayDeque<Integer> order = new ArrayDeque<>();
                    orderNum = 0;
                    deliver = new int[V+1];
                    deliverNum = 0;
                    int pos = 1;
                    path = new ArrayDeque<>();
                    StringBuilder command = new StringBuilder();
                    boolean returnToShop = false;
                    Map<Integer, ArrayDeque<Integer>> orderedTime = new HashMap<>();
                    for(int i = 2; i <= V; i++){
                        orderedTime.put(i, new ArrayDeque<>());
                    }
                    long score = 0;

                    for(int t = 0; t < tMax; t++){
                        if(info[t] != 0){
                            order.add(info[t]);
                            orderNum++;
                            orderedTime.get(info[t]).addLast(t);
                        }
                        if(!path.isEmpty()){
                            if(path.peek().cost == 1){
                                pos = path.poll().to;
                            }else{
                                path.peek().cost--;
                                pos = EDGE;
                            }
                        }
                        if(t == (9100 + b*50) && b >= 1) 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, c);
                                command.append(path.peek().to);
                            }
                        }else if(pos == EDGE){
                            command.append(path.peek().to);
                        }else{
                            if(deliver[pos] != 0){
                                deliverNum -= deliver[pos];
                                for(int i = 0; i < deliver[pos]; i++){
                                    int waitingTime = t - orderedTime.get(pos).poll();
                                    score += tMax * tMax - waitingTime * waitingTime;
                                }
                                deliver[pos] = 0;
                            }
                            if(returnToShop){
                                path.clear();
                                setPath(pos, SHOP, c);
                                returnToShop = false;
                            }else if(path.isEmpty()){
                                if(deliverNum == 0 || orderNum*40 > deliverNum*a){
                                    setPath(pos, SHOP, c);
                                }else{
                                    setPath(pos, -1, c);
                                }
                            }
                            command.append(path.peek().to);
                        }
                        command.append(System.lineSeparator());
                    }
                    if(score > maxScore){
                        maxScore = score;
                        bestCommand = command;
                    }
                }
            }
        }
        
        System.out.print(bestCommand);
    }
    
    static void setPath(int from, int to, int c){
        
        if(to == -1){
            for(Node n : nodeList.get(from)){
                if(deliver[n.id] != 0 || (n.id == SHOP && orderNum*15 > deliverNum*c)){
                    to = n.id;
                    break;
                }
            }
        }
        int v = from;
        while(v != to){
            path.addLast(new Move(next[v][to], dist[v][next[v][to]]));
            v = next[v][to];
        }
    }
    
    static class Node implements Comparable<Node>{
        int id;
        int dist;

        public Node(int id, int dist) {
            this.id = id;
            this.dist = dist;
        }

        @Override
        public int compareTo(Node n) {
            return this.dist - n.dist;
        }
    }
    
    static class Move {
        int to;
        int cost;

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