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: Runtime Error)

import java.io.*;
import java.util.*;

public class Main {
    //-------------------------------------------------------------//
    public static final void main(String[] args) {
        new Main().solve();
    }
    //-------------------------------------------------------------//
    private final Scanner sc = new Scanner(System.in);

    void solve() {
        int N = sc.nextInt();
        int M = sc.nextInt();
        List<Integer>[] g = new ArrayList[N];
        for (int i = 0; i < N; i++) g[i] = new ArrayList();
        for (int i = 0; i < M; i++) {
            int a = sc.nextInt() - 1;
            int b = sc.nextInt() - 1;
            g[a].add(b);
            g[b].add(a);
        }
        int Q = sc.nextInt();
        if (N > 2000 || M > 2000 || Q > 2000) System.exit(-1);
        int[] v = new int[N];
        Arrays.fill(v, 0);
        for (int i = 0; i < Q; i++) {
            Queue<Integer> vstk = new ArrayDeque<Integer>();
            Queue<Integer> dstk = new ArrayDeque<Integer>();
            vstk.add(sc.nextInt() - 1);
            dstk.add(0);
            int dist = sc.nextInt();
            int color = sc.nextInt();
            boolean[] visited = new boolean[N];
            Arrays.fill(visited, false);
            while (!vstk.isEmpty()) {
                int cv = vstk.poll();
                int d = dstk.poll();
                visited[cv] = true;
                v[cv] = color;
                if (d + 1 <= dist) {
                    for (int nv : g[cv]) if (!visited[nv]) {
                        vstk.add(nv);
                        dstk.add(d + 1);
                    }
                }
            }
        }
        for (int i = 0; i < N; i++) {
            System.out.println(v[i]);
        }
    }
}