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.*;
import java.math.*;
import java.util.*;

public class Main {
    private static boolean debug = false;
    private static boolean elapsed = false;

    private static PrintWriter _out = new PrintWriter(System.out);
    private static PrintWriter _err = new PrintWriter(System.err);

    private Map<Integer, Node> nodes = new HashMap<>();

    private boolean[][] memo;

    private static class Node {
        int no;
        List<Node> list = new ArrayList<>();
        int color;
        public Node(int no) {
            this.no = no;
        }
    }
    private static class Query {
        int v;
        int d;
        int c;
        public Query(int v, int d, int c) {
            this.v = v;
            this.d = d;
            this.c = c;
        }
    }
    private void solve(Scanner sc) {
        int N = sc.nextInt();
        int M = sc.nextInt();
        for (int i = 0; i < N; ++i) {
            nodes.put(i + 1, new Node(i + 1));
        }
        for (int i = 0; i < M; ++i) {
            int a = sc.nextInt();
            int b = sc.nextInt();
            nodes.get(a).list.add(nodes.get(b));
            nodes.get(b).list.add(nodes.get(a));
        }
        int Q = sc.nextInt();
        List<Query> queryList = new ArrayList<>();
        for (int i = 0; i < Q; ++i) {
            int v = sc.nextInt();
            int d = sc.nextInt();
            int c = sc.nextInt();
            Query query = new Query(v, d, c);
            queryList.add(query);
        }

        Collections.reverse(queryList);

        memo = new boolean[N + 1][11];

        for (Query query : queryList) {
            paint(query.v, query.d, query.c);
        }

        for (int i = 0; i < N; ++i) {
            _out.println(nodes.get(i + 1).color);
        }
    }
    private void paint(int v, int d, int c) {
        if (memo[v][d]) {
            return;
        }
        memo[v][d] = true;
        if (d == 0) {
            nodes.get(v).color = c;
            return;
        }

        Node node = nodes.get(v);
        paint(v, d - 1, c);
        for (Node child : node.list) {
            paint(child.no, d - 1, c);
        }
    }
    private static BigInteger C(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        for (long i = r; i > 1; --i) {
            res = res.divide(BigInteger.valueOf(i));
        }
        return res;
    }
    private static BigInteger P(long n, long r) {
        BigInteger res = BigInteger.ONE;
        for (long i = n; i > n - r; --i) {
            res = res.multiply(BigInteger.valueOf(i));
        }
        return res;
    }
    /*
     * 10^10 > Integer.MAX_VALUE = 2147483647 > 10^9
     * 10^19 > Long.MAX_VALUE = 9223372036854775807L > 10^18
     */
    public static void main(String[] args) {
        long S = System.currentTimeMillis();

        Scanner sc = new Scanner(System.in);
        new Main().solve(sc);
        _out.flush();

        long G = System.currentTimeMillis();
        if (elapsed) {
            _err.println((G - S) + "ms");
        }
        _err.flush();
    }
}