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.Closeable;
import java.io.IOException;
import java.io.InputStream;
import java.io.InputStreamReader;
import java.io.PrintWriter;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.HashMap;
import java.util.HashSet;
import java.util.LinkedList;
import java.util.Map.Entry;
import java.util.Scanner;
import java.util.StringTokenizer;
import java.util.TreeMap;

public class Main {
	
	public static void main(String[] args) throws IOException {
		final Scanner sc = new Scanner(System.in);
		
		final int N = sc.nextInt();
		final int M = sc.nextInt();
		
		ArrayList<HashMap<Integer, Integer>> adj = new ArrayList<HashMap<Integer, Integer>>();
		for(int i = 0; i < N; i++){ adj.add(new HashMap<Integer, Integer>()); }
		for(int i = 0; i < M; i++){
			final int a = sc.nextInt() - 1;
			final int b = sc.nextInt() - 1;
			
			adj.get(a).put(b, 1);
			adj.get(b).put(a, 1);
		}
		
		final int Q = sc.nextInt();
		int[] vs = new int[Q];
		int[] ds = new int[Q];
		int[] cs = new int[Q];
		for(int i = 0; i < Q; i++){
			vs[i] = sc.nextInt() - 1;
			ds[i] = sc.nextInt();
			cs[i] = sc.nextInt();
		}
		
		int[] colors = new int[N];
		Arrays.fill(colors, 0);
		
		boolean[] visited = new boolean[N];
		LinkedList<Integer> queue = new LinkedList<Integer>();
		LinkedList<Integer> frontier = new LinkedList<Integer>();
		
		for(int q = Q - 1; q >= 0; q--){
			final int v = vs[q];
			final int d = ds[q];
			final int c = cs[q];
			
			Arrays.fill(visited, false);
			
			queue.add(v);
			queue.add(d);
			visited[v] = true;
			
			while(!queue.isEmpty()){
				final int curr_v = queue.poll();
				final int curr_d = queue.poll();
				
				if(colors[curr_v] <= 0){ colors[curr_v] = c; }
				if(curr_d <= 0){ 
					frontier.add(curr_v);
					frontier.add(d - curr_d);
					continue;
				}
				
				boolean has_next = false;
				for(final int next_v : adj.get(curr_v).keySet()){
					if(visited[next_v]){ continue; }
					
					final int dist = adj.get(curr_v).get(next_v);
					if(dist > curr_d){ continue; }
					
					has_next = true;
					adj.get(curr_v).put(next_v, curr_d);
					visited[next_v] = true;
					
					queue.add(next_v);
					queue.add(curr_d - dist);
				}
				
				if(!has_next){ 
					frontier.add(curr_v);
					frontier.add(d - curr_d);
				}
				
				for(final int next_v : adj.get(curr_v).keySet()){
					adj.get(next_v).remove(curr_v);
				}
				adj.get(curr_v).clear();
			}
			
			while(!frontier.isEmpty()){
				final int edge = frontier.poll();
				final int cost = frontier.poll();
				if(edge == v){ continue; }
				
				adj.get(v).put(edge, cost);
				adj.get(edge).put(v, cost);
			}
			
			//System.out.println(adj);
		}
		
		try(PrintWriter pw = new PrintWriter(System.out)){
			for(int i = 0; i < N; i++){
				pw.println(colors[i]);
			}
			pw.flush();
		}
	}
	
	public static class Scanner implements Closeable {
		private BufferedReader br;
		private StringTokenizer tok;
 
		public Scanner(InputStream is) throws IOException {
			br = new BufferedReader(new InputStreamReader(is));
		}
 
		private void getLine() throws IOException {
			while (!hasNext()) {
				tok = new StringTokenizer(br.readLine());
			}
		}
 
		private boolean hasNext() {
			return tok != null && tok.hasMoreTokens();
		}
 
		public String next() throws IOException {
			getLine();
			return tok.nextToken();
		}
 
		public int nextInt() throws IOException {
			return Integer.parseInt(next());
		}
 
		public long nextLong() throws IOException {
			return Long.parseLong(next());
		}
 
		public double nextDouble() throws IOException {
			return Double.parseDouble(next());
		}
		
		public int[] nextIntArray(int n) throws IOException {
			final int[] ret = new int[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextInt();
			}
			return ret;
		}
		
		public long[] nextLongArray(int n) throws IOException {
			final long[] ret = new long[n];
			for(int i = 0; i < n; i++){
				ret[i] = this.nextLong();
			}
			return ret;
		}
 
		public void close() throws IOException {
			br.close();
		}
	}
}