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: Time Limit Exceeded)

import java.util.*;
 
public class Main{
	public static void main(String[] args){
		Scanner sc = new Scanner(System.in);
		int n = sc.nextInt();
		int m = sc.nextInt();
		int[] a = new int[2*m];
		int[] b = new int[2*m];
		int[] color = new int[n];
		int[][] dist = new int[n][n];
		for(int i=0;i<n;i++){
			color[i] = 0;
			for(int j=0;j<n;j++){
				dist[i][j] = Integer.MAX_VALUE;
			}
			dist[i][i] = 0;
		}
		
		int x;
		int y;
		
		for(int i=0;i<m;i++){
			a[2*i] = sc.nextInt()-1;
			b[2*i] = sc.nextInt()-1;
			a[2*i+1] = b[2*i];
			b[2*i+1] = a[2*i];
			dist[a[2*i]][b[2*i]] = 1;
			dist[b[2*i]][a[2*i]] = 1;
		}
		
		boolean changed = true;
		int kouho1=0;
		int kouho2=0;
		while(changed){
			changed = false;
			for(int i=0; i<2*m; i++){
				for(int j=0; j<n; j++){
					if(dist[a[i]][j] != Integer.MAX_VALUE){
						kouho1 = dist[a[i]][j]+1;
					}else{
						kouho1 = Integer.MAX_VALUE;
					}
					if(dist[b[i]][j] != Integer.MAX_VALUE){
						kouho2 = dist[b[i]][j]+1;
					}else{
						kouho2 = Integer.MAX_VALUE;
					}
					if(dist[a[i]][j] > kouho2){
						dist[a[i]][j] = kouho2;
						changed = true;
					}
					if(dist[b[i]][j] > kouho1){
						dist[b[i]][j] = kouho1;
						changed = true;
					}
				}
			}
		}
			
		int q = sc.nextInt();
		int v;
		int d;
		int c;
		for(int i=0; i<q; i++){
			v = sc.nextInt()-1;
			d = sc.nextInt();
			c = sc.nextInt();
			for(int j=0; j<n; j++){
				if(dist[v][j]<=d){
					color[j] = c;
				}
			}
			/*for(int j=0; j<n; j++){
				System.out.println(color[j]);
			}*/
		}
		
		/*for(int i=0;i<n;i++){
			for(int j=i+1;j<n;j++){
				System.out.println("dist["+i+"]["+j+"] = "+dist[i][j]);
			}
		}*/
		
		
		for(int i=0; i<n; i++){
			System.out.println(color[i]);
		}
		return;
	}
}