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.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.io.PrintStream;
import java.util.Collection;
import java.io.IOException;
import java.io.InputStreamReader;
import java.util.StringTokenizer;
import java.io.BufferedReader;
import java.util.Queue;
import java.util.LinkedList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 *
 * @author Wolfgang Beyer
 */
public class Main {
    public static void main(String[] args) {
        InputStream inputStream = System.in;
        OutputStream outputStream = System.out;
        InputReader in = new InputReader(inputStream);
        PrintWriter out = new PrintWriter(outputStream);
        SplatterPainting solver = new SplatterPainting();
        solver.solve(1, in, out);
        out.close();
    }

    static class SplatterPainting {
        int[][] g;
        int[] nodeColor;
        int[] coloredDistance;
        int n;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            n = in.nextInt();
            int m = in.nextInt();
            int[] u = new int[m];
            int[] v = new int[m];
            int[] degree = new int[n];
            for (int i = 0; i < m; i++) {
                u[i] = in.nextInt() - 1;
                v[i] = in.nextInt() - 1;
                degree[u[i]]++;
                degree[v[i]]++;
            }
            int q = in.nextInt();
            int[] origin = new int[q];
            int[] dist = new int[q];
            int[] color = new int[q];
            for (int i = 0; i < q; i++) {
                origin[i] = in.nextInt() - 1;
                dist[i] = in.nextInt();
                color[i] = in.nextInt();
            }

            g = new int[n][];
            for (int i = 0; i < n; i++) {
                g[i] = new int[degree[i]];
            }
            int[] pointers = new int[n];
            for (int i = 0; i < m; i++) {
                g[u[i]][pointers[u[i]]++] = v[i];
                g[v[i]][pointers[v[i]]++] = u[i];
            }

            nodeColor = new int[n];
            coloredDistance = new int[n];

            for (int i = q - 1; i >= 0; i--) {
                bfs(origin[i], dist[i], color[i]);
            }

            for (int i = 0; i < n; i++) {
                out.println(nodeColor[i] + " ");
            }
        }

        void bfs(int node, int dist, int color) {
            boolean[] visited = new boolean[n];
            Queue<Element> stack = new LinkedList<>();
            stack.add(new Element(node, dist));
            visited[node] = true;
            while (!stack.isEmpty()) {
                Element currentElement = stack.remove();
                if (nodeColor[currentElement.node] == 0) {
                    nodeColor[currentElement.node] = color;
                }
                if (currentElement.dist > coloredDistance[currentElement.node]) {
                    coloredDistance[currentElement.node] = currentElement.dist;
                    for (int neighbor : g[currentElement.node]) {
                        if (!visited[neighbor]) {
                            stack.add(new Element(neighbor, currentElement.dist - 1));
                            visited[neighbor] = true;
                        }
                    }
                }
            }
        }

        class Element {
            int node;
            int dist;

            public Element(int n, int d) {
                node = n;
                dist = d;
            }

        }

    }

    static class InputReader {
        private static BufferedReader in;
        private static StringTokenizer tok;

        public InputReader(InputStream in) {
            this.in = new BufferedReader(new InputStreamReader(in));
        }

        public int nextInt() {
            return Integer.parseInt(next());
        }

        public String next() {
            try {
                while (tok == null || !tok.hasMoreTokens()) {
                    tok = new StringTokenizer(in.readLine());
                    //tok = new StringTokenizer(in.readLine(), ", \t\n\r\f"); //adds commas as delimeter
                }
            } catch (IOException ex) {
                System.err.println("An IOException was caught :" + ex.getMessage());
            }
            return tok.nextToken();
        }

    }
}