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.util.*;
public class Main {
	public static void main(String[] args) {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		int M = sc.nextInt();
		V[] vs = new V[N];
		for (int i = 0; i < N; i++) {
			vs[i] = new V(i);
		}
		for (int i = 0; i < M; i++) {
			int s = sc.nextInt() - 1;
			int t = sc.nextInt() - 1;
			vs[s].add(t);
			vs[t].add(s);
		}
		int Q = sc.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] = sc.nextInt() - 1;
			d[i] = sc.nextInt();
			c[i] = sc.nextInt();
		}
		dist = new int[N];
		Arrays.fill(dist, -1);
		for (int i = Q - 1; i >= 0; i--) {
			color(vs, v[i], d[i], c[i]);
		}
		Arrays.stream(vs).forEach(u -> System.out.println(u.col));
	}
	static int dist[];
	private static void color(V[] vs, int s, int d, int c) {
		if (dist[s] >= d) {
			return;
		}
		Queue<Integer> que = new LinkedList<>();
		que.add(s);
		dist[s] = d;
		while(que.isEmpty() == false) {
			int u = que.poll();
			if (vs[u].col == 0) { 
				vs[u].col = c;
			}
			if (dist[u] == 0) {
				continue;
			}
			for (int v: vs[u]) {
				if (dist[v] >= dist[u] - 1) {
					continue;
				}
				que.add(v);
				dist[v] = dist[u] - 1;
			}
		}
	}
	static class V extends ArrayList<Integer>{
		int id;
		int col = 0;
		V(int _id) {
			id = _id;
		}
	}
}