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 C# (Mono 4.6.2.0) (judge verdict: Runtime Error)

using System;
using System.Collections.Generic;
public class Aprob {
    public static void Main() {
        string[] readSome = new string[2];
        readSome = Console.ReadLine().Split(' ');
        int N = int.Parse(readSome[0]);
        int M = int.Parse(readSome[1]);
        int a;
        int b;
        int[,] dis = new int[N+1, N+1];
        for (int i = 0; i < M; i++) {
            readSome = Console.ReadLine().Split(' ');
            a = int.Parse(readSome[0]);
            b = int.Parse(readSome[1]);
            dis[a, b] = 1;
            dis[b, a] = 1;
        }
        for (int i = 1; i <= N; i++) {
            dis[i, i] = -1;
        }
        int Q = int.Parse(Console.ReadLine());
        readSome = new string[3];
        int[] v = new int[Q];
        int[] d = new int[Q];
        int[] c = new int[Q];
        int[] color = new int[N+1];
        int max = 0;
        for (int i = 0; i < Q; i++) {
            readSome = Console.ReadLine().Split(' ');
            v[i] = int.Parse(readSome[0]);
            d[i] = int.Parse(readSome[1]);
            c[i] = int.Parse(readSome[2]);
            max = Math.Max(max, d[i]);
        }
        for (int i = 1; i < max; i++) {
            dis = diss(N, i, dis);
        }
        /*string outp = "";
        for (int i = 1; i <= N; i++) {
            outp = "";
            for (int j = 1; j <= N; j++) {
                outp += dis[i, j] + ",";
            }
            Console.WriteLine(outp);
        }*/
        for (int i = 0; i < Q; i++) {
            for (int j = 1; j <= N; j++) {
                if (dis[v[i], j] <= d[i] & dis[v[i], j] != -0) {
                    color[j] = c[i];
                }
            }
        }
        for (int i = 1; i <= N; i++) {
            Console.WriteLine(color[i]);
        }
    }
    public static int[,] diss(int N,int now,int[,]dis) {
        for (int i = 1; i <= N; i++) {
            for (int j = 1; j <= N; j++) {
                if (dis[i, j] == now) {
                    for (int k = 1; k <= N; k++) {
                        if (dis[j, k] == 1&dis[i,k]==0) {
                            dis[i, k] = now + 1;
                        }
                    }
                }
            }
        }
        return dis;
    }
}