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: Accepted)

using System;
using System.Linq;//リストの使用
using System.Collections.Generic;
using System.Text;//テキストの高速出力に必要
class Solve
{
  List<int>[] G;
  int[] color;
  int[] us;//拡大可能距離
  StringBuilder sb;//解答
  
  public static void Main()
  {
    new Solve().Run();
  }
  
  void Run()
  {
    sb = new StringBuilder();
    Calc();
    Console.Write(sb.ToString());
  }
  
  void Calc()
  {
    string[] str = Console.ReadLine().Split(' ');
    int N = int.Parse(str[0]);
    int M = int.Parse(str[1]);
    G = new List<int>[N];//隣接リスト
    for(int i = 0; i < N; i++) G[i] = new List<int>();
    for(int i = 0; i < M; i++)//隣接リストの作成
    {
      str = Console.ReadLine().Split(' ');
      int a = int.Parse(str[0]) - 1;//頂点番号は1減らして受け取る
      int b = int.Parse(str[1]) - 1;
      G[a].Add(b);
      G[b].Add(a);
    }
      
    int Q = int.Parse(Console.ReadLine());
    int[] V = new int[Q];//各クエリを受け取る
    int[] D = new int[Q];
    int[] C = new int[Q];
    for(int i = 0; i < Q; i++)
    {
      str = Console.ReadLine().Split(' ');
      V[i] = int.Parse(str[0])-1;
      D[i] = int.Parse(str[1]);
      C[i] = int.Parse(str[2]);
    }
      
    color = new int[N];
    us = new int[N];
    for(int i = 0; i < N; i++) us[i] = -1;//初期化
    
    for(int i = Q-1; i >= 0; i--)//クエリを逆順に処理
    {
      if(us[V[i]] < D[i])//拡大可能距離を増やせるならば
      {
        dfs(V[i],D[i],C[i]);//深さ優先探索を繰り返す
      }
    }
    
    for(int i = 0; i < N; i++) sb.Append(color[i]+"\n");//出力メモ
  }
    
  void dfs(int v,int d,int c)//深さ優先探索
  {
    us[v] = d;//拡大可能距離
    if(color[v] == 0) color[v] = c;//塗っていない時だけ上書き
    if(d != 0)//周りも塗れる可能性がある時
    {
      for(int i = 0; i < G[v].Count; i++)//隣接頂点の確認
      {
        int t = G[v][i];
        if(us[t] < d-1) dfs(t,d-1,c);
      }
    }
  }
}