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.*;

public class Main{
    
    static int[] v,d,c,result,used;
    
    public static void main(String[] args){
        Scanner sc = new Scanner(System.in);
        
        final int mod = ((int)1e9)+7;
        
        int n = Integer.parseInt(sc.next());
        int m = Integer.parseInt(sc.next());
        
        ArrayList<Integer>[] g = new ArrayList[n];
        for(int i=0; i<n; i++){
            g[i] = new ArrayList<>();
        }
        
        for(int i=0; i<m; i++){
            int a = Integer.parseInt(sc.next())-1;
            int b = Integer.parseInt(sc.next())-1;
            g[a].add(b);
            g[b].add(a);
        }
        
        //
        int q = Integer.parseInt(sc.next());
        v = new int[q];
        d = new int[q];
        c = new int[q];
        
        for(int i=0; i<q; i++){
            v[i] = Integer.parseInt(sc.next())-1;
            d[i] = Integer.parseInt(sc.next());
            c[i] = Integer.parseInt(sc.next());
        }
        
        //
        result = new int[n];
        used = new int[n];
        Arrays.fill(used, -1);
        
        for(int t=q-1; t>=0; t--){
            ArrayDeque<Integer> que = new ArrayDeque();
            push(t, v[t], d[t], que);
            
            while(que.size() != 0){
                int i = que.pollFirst();
                if(used[i] != 0){
                    for(int j=0; j<g[i].size(); j++){
                        push(t, g[i].get(j), used[i]-1, que);
                    }
                }
            }
        }
        
        //
        for(int i=0; i<n; i++){
            System.out.println(result[i]);
        }
        
    }
    
    public static void push(int t, int i, int dist, ArrayDeque<Integer> que){
        if(used[i] < dist){
            used[i] = dist;
            if(result[i] == 0){
                result[i] = c[t];
            }
            que.offerLast(i);
        }
    }
}