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: Accepted)

import java.util.ArrayList;
import java.util.Arrays;
import java.util.Scanner;

public class Main {

	static Scanner scan = new Scanner(System.in);
	static int N = scan.nextInt();
	static int M = scan.nextInt();
	static int dp[]=new int[N];//メモ化
	static int count;







	public static void paint(int v,int c,V vs[]){
		if(dp[v]>=count){return;}//来たことがあってより深くまで塗れないなら帰る
		if(vs[v].color==0){
			vs[v].color=c;
		}
		dp[v]=count;
		if(count>0){
			count--;
			for(int j=0;j<vs[v].size();j++){
				paint(vs[v].get(j),c,vs);
		}
			count++;
		}



	}

	public static void main(String[] args) {
		// TODO 自動生成されたメソッド・スタブ

		V vs[] = new V[N];
		for(int i =0;i<N;i++){
			vs[i] = new V(i);
		}


		int a;
		int b;

		for(int i =0;i<M;i++){
			a=scan.nextInt()-1;
			b=scan.nextInt()-1;

			vs[a].add(b);
			vs[b].add(a);
		}

		int Q = scan.nextInt();
		int v[] = new int[Q];
		int d[] = new int[Q];
		int c[] = new int[Q];

		for(int i =0;i<Q;i++){
			v[i]=scan.nextInt() - 1;
			d[i]=scan.nextInt();
			c[i]=scan.nextInt();
		}

		Arrays.fill(dp, -1);
		//ここから塗りつぶし動作
		for(int i =Q-1;i>=0;i--){
			count = d[i];
					paint(v[i],c[i],vs);

			}

		for(int i=0;i<N;i++){
			System.out.println(vs[i].color);
		}

		}

	static class V extends ArrayList<Integer>{
		int id;
		int color = 0;
		V(int _id){
			id = _id;
		}
	}



	}