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 Java7 (OpenJDK 1.7.0) (judge verdict: Accepted)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;
 
public class Main {
    private void solve() {
        Scanner sc = new Scanner(System.in);
        int n = sc.nextInt();
        int m = sc.nextInt();
        ArrayList<Integer>[] adjList = new ArrayList[n];
        int[] a = new int[m];
        int[] b = new int[m];
        for (int i = 0; i < n; i++) {
            adjList[i] = new ArrayList<>();
        }
        for (int i = 0; i < m; i++) {
            a[i] = sc.nextInt() - 1;
            b[i] = sc.nextInt() - 1;
            adjList[a[i]].add(b[i]);
            adjList[b[i]].add(a[i]);
        }
 
        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();
        }
 
        boolean[][] visited = new boolean[n][11];
        int[] color = new int[n];
        Arrays.fill(color, -1);
        for (int i = q - 1; i >= 0; i--) {
            dfs(adjList, visited, color, v[i], d[i], c[i]);
        }
        for (int clr : color) {
            System.out.println(clr == -1 ? 0 : clr);
        }
    }
 
    private void dfs(ArrayList<Integer>[] adjList, boolean[][] visited, int[] color, int v, int d, int c) {
        if (visited[v][d]) {
            return;
        }
        if (color[v] == -1 && d == 0) {
            color[v] = c;
        } else {
            dfs(adjList, visited, color, v, d - 1, c);
            for (int adj : adjList[v]) {
                dfs(adjList, visited, color, adj, d - 1, c);
            }
        }
        visited[v][d] = true;
    }
 
    public static void main(String[] args) {
        // new B_SplatterPainting().solve();
        new Main().solve();
    }
}