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: Wrong Answer)

import java.math.BigInteger;
import java.util.ArrayList;
import java.util.Arrays;
import java.util.Collections;
import java.util.List;
import java.util.Scanner;

public class Main {

	public Main() {
		// TODO Auto-generated constructor stub
	}

	public static void main(String[] args) {
		SplatterPainting sp = new SplatterPainting();
		sp.run();
	}

}

class SplatterPainting {
	
	class Vertex {
		
		int id;
		ArrayList<Vertex> neighbours;
		int color;
		
		public Vertex(int id) {
			neighbours = new ArrayList<>();
			color = 0;
			this.id = id;
		}
	}
	
	boolean[] isPainted; 
	Vertex[] vertices;
	
	public SplatterPainting() {
		
	}
	
	public void run() {
		Scanner sc = new Scanner(System.in);
		int N = sc.nextInt();
		vertices = new Vertex[N + 1];
		int M = sc.nextInt();
		for(int i = 1; i < N + 1; i++)
			vertices[i] = new Vertex(i); 
		for(int i = 0; i < M; i++) {
			int a = sc.nextInt();
			int b = sc.nextInt();
			vertices[a].neighbours.add(vertices[b]);
			vertices[b].neighbours.add(vertices[a]);
		}
		int Q = sc.nextInt();
		for(int i = 0; i < Q; i++) {
			int v = sc.nextInt();
			int d = sc.nextInt();
			int c = sc.nextInt();
			isPainted = new boolean[N + 1];
			paint(vertices[v], d, c);
		}
		sc.close();
		for(int i = 1; i < N + 1; i++)
			System.out.println(vertices[i].color);
	}
	
	public void paint(Vertex from, int distance, int color) {
		from.color = color;
		isPainted[from.id] = true;
		if(distance == 0)
			return;
		for(int i = 0; i < from.neighbours.size(); i++) {
			if(!isPainted[from.neighbours.get(i).id]) {
				paint(from.neighbours.get(i), distance - 1, color);
			}
		}
	}
}