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: Accepted)

using System.Collections.Generic;
using System.IO;
using System.Linq;
using System;
using static System.Math;
using static System.Console;

class E { static void Main() => new J(); }
class J
{
	int F() => int.Parse(ReadLine());
	int[] G() => ReadLine().Split(new char[] { ' ', '\t' }, StringSplitOptions.RemoveEmptyEntries).Select(int.Parse).ToArray();
	public J()
	{
		SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
		var I = G();
		int V = I[0], E = I[1], D = 10;
		var es = new List<int>[V];
		for (var u = 0; u < V; u++) es[u] = new List<int> { u };
		for (var e = 0; e < E; e++)
		{
			I = G();
			int a = I[0] - 1, b = I[1] - 1;
			es[a].Add(b);
			es[b].Add(a);
		}
		var Q = F();
		var col = new int[Q + 1];
		var dp = new int[V, D + 1];
		for (var q = 0; q < Q; q++)
		{
			I = G();
			col[q + 1] = I[2];
			int u = I[0] - 1, d = I[1];
			dp[u, d] = Max(dp[u, d], q + 1);
		}
		for (var d = D; d > 0; d--) for (var u = 0; u < V; u++) foreach (var v in es[u]) dp[v, d - 1] = Max(dp[v, d - 1], dp[u, d]);
		for (var u = 0; u < V; u++) WriteLine(col[dp[u, 0]]);
		Out.Flush();
	}
}