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.IOException;
import java.io.InputStream;
import java.io.PrintWriter;
import java.util.*;

public class Main {

    public static void main(String[] args) {
        new Main().solve();
    }

    void solve() {
        InputReader in = new InputReader(System.in);
        PrintWriter out = new PrintWriter(System.out);
        int n = in.nextInt();
        int m = in.nextInt();
        List<Integer> edges[] = new List[n];
        for (int i = 0; i < n; ++i) {
            edges[i] = new ArrayList<>();
        }
        for (int i = 0; i < m; ++i) {
            int a = in.nextInt() - 1;
            int b = in.nextInt() - 1;
            edges[a].add(b);
            edges[b].add(a);
        }
        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();
        }
        int color[] = new int[n];
        int dist[] = new int[n];
        for (int i = q - 1; i >= 0; --i) {
            class Vertex {
                int v, d, c;

                Vertex(int v, int d, int c) {
                    this.v = v;
                    this.d = d;
                    this.c = c;
                }
            }
            Queue<Vertex> queue = new ArrayDeque<>();
            queue.add(new Vertex(v[i], d[i], c[i]));
            while (queue.size() > 0) {
                Vertex x = queue.poll();
                if (color[x.v] == 0) color[x.v] = x.c;
                if (dist[x.v] < x.d) {
                    for (Integer k : edges[x.v]) {
                        queue.add(new Vertex(k, x.d - 1, x.c));
                    }
                    dist[x.v] = x.d;
                }
            }
        }
        for (int i = 0; i < n; ++i) {
            out.println(color[i]);
        }
        out.flush();
    }

    class InputReader {
        private InputStream stream;
        private byte[] buf = new byte[1024];
        private int curChar;
        private int numChars;

        public InputReader(InputStream stream) {
            this.stream = stream;
        }

        public int next() {
            if (numChars == -1) throw new InputMismatchException();
            if (curChar >= numChars) {
                curChar = 0;
                try {
                    numChars = stream.read(buf);
                } catch (IOException e) {
                    throw new InputMismatchException();
                }
                if (numChars <= 0) return -1;
            }
            return buf[curChar++];
        }

        public int nextInt() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            int sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            int res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public long nextLong() {
            int c = next();
            while (isSpaceChar(c))
                c = next();
            long sgn = 1;
            if (c == '-') {
                sgn = -1;
                c = next();
            }
            long res = 0;
            do {
                if (c < '0' || c > '9') throw new InputMismatchException();
                res *= 10;
                res += c - '0';
                c = next();
            } while (!isSpaceChar(c));
            return res * sgn;
        }

        public boolean isSpaceChar(int c) {
            return c == ' ' || c == '\n' || c == '\r' || c == '\t' || c == -1;
        }
    }
}