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: Accepted)

import java.io.OutputStream;
import java.io.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.StringTokenizer;
import java.io.IOException;
import java.util.InputMismatchException;
import java.io.BufferedReader;
import java.io.InputStreamReader;
import java.util.ArrayList;
import java.io.InputStream;

/**
 * Built using CHelper plug-in
 * Actual solution is at the top
 */
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);
        TaskB solver = new TaskB();
        solver.solve(1, in, out);
        out.close();
    }

    static class TaskB {
        ArrayList<Integer>[] G;
        int[][] dp;

        public void solve(int testNumber, InputReader in, PrintWriter out) {
            int n = in.nextInt();
            int m = in.nextInt();
            int[] a = new int[m];
            int[] b = new int[m];
            for (int i = 0; i < m; i++) {
                a[i] = in.nextInt() - 1;
                b[i] = in.nextInt() - 1;
            }
            int q = in.nextInt();
            int[] v = new int[q];
            int[] d = new int[q];
            int[] c = new int[q];
            for (int i = 0; i < q; i++) {
                v[i] = in.nextInt() - 1;
                d[i] = in.nextInt();
                c[i] = in.nextInt();
            }

            G = new ArrayList[n];
            for (int i = 0; i < n; i++) {
                G[i] = new ArrayList<>();
            }
            for (int i = 0; i < m; i++) {
                G[a[i]].add(b[i]);
                G[b[i]].add(a[i]);
            }

            dp = new int[100010][11];

            for (int i = q - 1; i >= 0; i--) {
                rec(v[i], d[i], c[i]);
            }

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

        void rec(int v, int d, int c) {
            if (dp[v][d] > 0) return;

            dp[v][d] = c;
            if (d == 0) return;

            for (int to : G[v]) {
                rec(to, d - 1, c);
            }
            rec(v, d - 1, c);
        }

    }

    static class InputReader {
        BufferedReader in;
        StringTokenizer tok;

        public String nextString() {
            while (!tok.hasMoreTokens()) {
                try {
                    tok = new StringTokenizer(in.readLine(), " ");
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
            }
            return tok.nextToken();
        }

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

        public InputReader(InputStream inputStream) {
            in = new BufferedReader(new InputStreamReader(inputStream));
            tok = new StringTokenizer("");
        }

    }
}