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: Time Limit Exceeded)

using System;
using System.Collections;
using System.Collections.Generic;
using System.Linq;
using System.Text;

class TEST{
	static void Main(){
		Sol mySol =new Sol();
		mySol.Solve();
	}
}

class Sol{
	public void Solve(){
		
		List<int>[] E = new List<int>[N];
		for(int i=0;i<N;i++) E[i] = new List<int>();
		for(int i=0;i<M;i++){
			E[A[i]].Add(B[i]);
			E[B[i]].Add(A[i]);
		}
		
		int[] ans = new int[N];
		bool[] used = new bool[N];
		int cnt = 0;
		int Inf = (int)1e9;
		for(int q=Q-1;q>=0;q--){
			int[] dist = new int[N];
			for(int j=0;j<N;j++) dist[j] = Inf;
			Queue<int> Qu = new Queue<int>();
			Qu.Enqueue(V[q]);
			dist[V[q]] = 0;
			if(!used[V[q]]){
				ans[V[q]] = C[q];
				used[V[q]] = true;
				cnt++;
				if(cnt == N){
					Console.WriteLine(String.Join("\n",ans));
					return;
				}
			}
			while(Qu.Count>0){
				var now = Qu.Dequeue();
				if(dist[now] >= D[q]) continue;
				foreach(var nxt in E[now]){
					if(dist[nxt] == Inf){
						dist[nxt] = dist[now] + 1;
						if(!used[nxt]){
							ans[nxt] = C[q];
							used[nxt] = true;
							if(cnt == N){
								Console.WriteLine(String.Join("\n",ans));
								return;
							}
						}
						Qu.Enqueue(nxt);
					}
				}
			}
			//Console.WriteLine(String.Join(" ",dist));
		}
		
		Console.WriteLine(String.Join("\n",ans));
		
	}
	int N,M;
	int[] A,B;
	int Q;
	int[] V,D,C;
	public Sol(){
		var d = ria();
		N = d[0]; M = d[1];
		A = new int[M];
		B = new int[M];
		for(int i=0;i<M;i++){
			d = ria();
			A[i] = d[0] - 1; B[i] = d[1] - 1;
		}
		Q = ri();
		V = new int[Q];
		D = new int[Q];
		C = new int[Q];
		for(int i=0;i<Q;i++){
			d = ria();
			V[i] = d[0] - 1; D[i] = d[1]; C[i] = d[2];
		}
		
	}

	static String rs(){return Console.ReadLine();}
	static int ri(){return int.Parse(Console.ReadLine());}
	static long rl(){return long.Parse(Console.ReadLine());}
	static double rd(){return double.Parse(Console.ReadLine());}
	static String[] rsa(char sep=' '){return Console.ReadLine().Split(sep);}
	static int[] ria(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>int.Parse(e));}
	static long[] rla(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>long.Parse(e));}
	static double[] rda(char sep=' '){return Array.ConvertAll(Console.ReadLine().Split(sep),e=>double.Parse(e));}
}