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: Wrong Answer)


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

public class Main {

	public static void main(String[] args) throws IOException {
		InputStream inputStream = System.in;
		OutputStream outputStream = System.out;
		InputReader in = new InputReader(inputStream);
		PrintWriter out = new PrintWriter(outputStream);
		TaskX solver = new TaskX();
		solver.solve(1, in, out);
		out.close();
	}

	static int INF = 1 << 30;
	static int modP = 1000000007;

	static class TaskX {
		public void solve(int testNumber, InputReader in, PrintWriter out) {

			int n = in.nextInt();
			Node[] nodes = new Node[n];
			for (int i = 0; i < n; i++) {
				nodes[i] = new Node(i);
			}

			int m = in.nextInt();
			List<Integer>[] list = new ArrayList[n];
			for (int i = 0; i < n; i++) {
				list[i] = new ArrayList<>();
			}
			for (int i = 0; i < m; i++) {
				int a = in.nextInt()-1;
				int b = in.nextInt()-1;
				list[a].add(b);
				list[b].add(a);
			}


			// solve
			int q = in.nextInt();
			int[][] info = new int[q][3];
			for (int i = 0; i < q; i++) {
				int v = in.nextInt()-1;
				int d = in.nextInt();
				int c = in.nextInt();

				info[i][0] = v;
				info[i][1] = d;
				info[i][2] = c;
			}

			for (int i = 0; i < q; i++) {

				int v = info[i][0];
				int d = info[i][1];
				int c = info[i][2];

				Queue<Node> queue = new ArrayDeque<>();
				nodes[v].cost = 0;
				nodes[v].color = c;
				queue.add(nodes[v]);

				while (!queue.isEmpty()) {

					Node fnode = queue.remove();

					for (int j = 0; j < list[fnode.num].size(); j++) {
						int tnode = list[fnode.num].get(j);
						int tcost = nodes[fnode.num].cost + 1;

						if (tcost <= d) {
							nodes[tnode].cost = tcost;
							nodes[tnode].color = c;
							queue.add(nodes[tnode]);
						}
					}
				}
			}

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

		}
	}

	static class Node {
		int num, cost, color;
		Node (int num) {
			this.num = num;
		}
	}

	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 long nextLong() {
			return Long.parseLong(nextString());
		}

		public double nextDouble() {
			return Double.parseDouble(nextString());
		}

		public int[] nextIntArray(int n) {
			int[] res = new int[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextInt();
			}
			return res;
		}

		public long[] nextLongArray(int n) {
			long[] res = new long[n];
			for (int i = 0; i < n; i++) {
				res[i] = nextLong();
			}
			return res;
		}

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

	}

}