Problem:
Score : 700 points

Problem Statement

Squid loves painting vertices in graphs.

There is a simple undirected graph consisting of N vertices numbered 1 through N, and M edges.
Initially, all the vertices are painted in color 0. The i-th edge bidirectionally connects two vertices a_i and b_i. The length of every edge is 1.

Squid performed Q operations on this graph. In the i-th operation, he repaints all the vertices within a distance of d_i from vertex v_i, in color c_i.

Find the color of each vertex after the Q operations.

Constraints

1 ≤ N,M,Q ≤ 10^5

1 ≤ a_i,b_i,v_i ≤ N

a_i ≠ b_i

0 ≤ d_i ≤ 10

1 ≤ c_i ≤10^5

d_i and c_i are all integers.

There are no self-loops or multiple edges in the given graph.

Partial Score

200 points will be awarded for passing the testset satisfying 1 ≤ N,M,Q ≤ 2{,}000.

Input

Input is given from Standard Input in the following format:

N M
a_1 b_1
:
a_{M} b_{M}
Q
v_1 d_1 c_1
:
v_{Q} d_{Q} c_{Q}

Output

Print the answer in N lines.
In the i-th line, print the color of vertex i after the Q operations.

Sample Input 1

7 7
1 2
1 3
1 4
4 5
5 6
5 7
2 3
2
6 1 1
1 2 2

Sample Output 1

2
2
2
2
2
1
0

Initially, each vertex is painted in color 0.
In the first operation, vertices 5 and 6 are repainted in color 1.
In the second operation, vertices 1, 2, 3, 4 and 5 are repainted in color 2.

Sample Input 2

14 10
1 4
5 7
7 11
4 10
14 7
14 3
6 14
8 11
5 13
8 3
8
8 6 2
9 7 85
6 9 3
6 7 5
10 3 1
12 9 4
9 6 6
8 2 3

Sample Output 2

1
0
3
1
5
5
3
3
6
1
3
4
5
3

The given graph may not be connected.

Solution in Java8 (OpenJDK 1.8.0) (judge verdict: Time Limit Exceeded)

import java.io.BufferedReader;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.LinkedList;
import java.util.PriorityQueue;
import java.util.Queue;

public class Main {
    public static void main(String[] args) {
        int n = 0, m = 0, q = 0;
        boolean[][] edges = null;
        operator[] ops = null;
        try (BufferedReader br = new BufferedReader(new InputStreamReader(System.in))) {
            String[] elems = br.readLine().split(" ");
            n = Integer.parseInt(elems[0]);
            m = Integer.parseInt(elems[1]);
            edges = new boolean[n][n];
            int v1, v2;
            for (int i = 0; i < m; i++) {
                elems = br.readLine().split(" ");
                v1 = Integer.parseInt(elems[0]) - 1;
                v2 = Integer.parseInt(elems[1]) - 1;
                edges[v1][v2] = edges[v2][v1] = true;
            }
            elems = br.readLine().split(" ");
            q = Integer.parseInt(elems[0]);
            ops = new operator[q];
            int v, d, c;
            for (int i = 0; i < q; i++) {
                elems = br.readLine().split(" ");
                v = Integer.parseInt(elems[0]) - 1;
                d = Integer.parseInt(elems[1]);
                c = Integer.parseInt(elems[2]);
                ops[i] = new operator(v, d, c);
            }
        } catch (IOException e) {
            e.printStackTrace();
        }
        int[] colors = new int[n];
        Queue<node> queue = new PriorityQueue<>((s1, s2) ->
                Integer.compare(s1.cost, s2.cost));
        int[][] memo = new int[n][n];
        for (int i = 0; i < memo.length; i++) {
            for (int j = 0; j < memo.length; j++) {
                memo[i][j] = n + 1;
            }
        }
        for (int i = 0; i < n; i++) {
            queue.clear();
            int[] dist = new int[n];
            for (int j = 0; j < n; j++){
                dist[j] = Integer.MAX_VALUE;
            }
            dist[i] = 0;
            node start = new node(i, 0, 0);
            queue.add(start);
            while (!queue.isEmpty()) {
                node trg = queue.poll();
                if (dist[trg.current] != trg.cost)
                    continue;
                int current = trg.current;
                for (int j = 0; j < n; j++){
                    if(edges[current][j] == false)
                        continue;
                    int tmp = trg.cost + 1;
                    if (dist[j] > tmp) {
                        queue.add(new node(j, current, tmp));
                        dist[j] = tmp;
                    }
                }
            }
            for (int k = 0; k < dist.length; k++) {
                memo[i][k] = dist[k];
            }
        }
        for (operator o : ops) {
            for (int i = 0; i < n; i++) {
                if (memo[o.vertex][i] <= o.dist)
                    colors[i] = o.color;
            }
        }
        for (int c : colors)
            System.out.println(c);
    }

    static class operator {
        int vertex;
        int dist;
        int color;
        operator(int v, int d, int c) {
            vertex = v;
            dist = d;
            color = c;
        }
    }

    static class node {
        int prev;
        int current;
        int cost;
        node (int current, int prev, int cost) {
            this.prev = prev;
            this.current = current;
            this.cost = cost;
        }
    }
}