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: Runtime Error)

using System;
using System.Collections.Generic;
using System.Linq;
using System.Text;
using System.Threading.Tasks;

namespace Splatter
{
    class Program
    {
        static void Main(string[] args)
        {
            int N, M;
            string[] vals = Console.ReadLine().Split(' ');
            N = int.Parse(vals[0]);
            M = int.Parse(vals[1]);
            int[,] dist = new int[N + 1, N + 1];
            for(int i=1; i<= N; i++)
            {
                for(int j=1; j<= N; j++)
                {
                    if (i == j)
                        dist[i, j] = 0;
                    else
                        dist[i, j] = 100001;
                }
            }

            for(int m=0; m< M; m++)
            {
                vals = Console.ReadLine().Split(' ');
                int a = int.Parse(vals[0]);
                int b = int.Parse(vals[1]);
                dist[a, b] = 1;
                dist[b, a] = 1;
            }

            for(int k=1; k <= N; k++)
            {
                for(int i = 1; i<= N; i++)
                {
                    for(int j = 1; j<= N; j++)
                    {
                        dist[i, j] = Math.Min(dist[i, j], dist[i, k] + dist[k, j]);
                    }
                }
            }
            List<int>[,] distList = new List<int>[N + 1, N + 1];
            for (int i = 1; i <= N; i++)
                for (int v = 0; v <= N; v++)
                    distList[i, v] = new List<int>();
            for(int i=1; i<= N; i++)
            {
                for(int j=1; j<= N; j++)
                {
                    //Console.WriteLine("dist[" + i + "," + j + "]" + "=" + dist[i, j]);
                    if(dist[i,j] <= 100000)
                        distList[i, dist[i, j]].Add(j);
                }
            }

            int Q = int.Parse(Console.ReadLine());
            int[] color = new int[N + 1];
            for(int q=0; q < Q; q++)
            {
                int v, d, c;
                vals = Console.ReadLine().Split(' ');
                v = int.Parse(vals[0]);
                d = int.Parse(vals[1]);
                c = int.Parse(vals[2]);
                for(int e = 0; e <= d; e++)
                {
                    foreach (int w in distList[v, e])
                        color[w] = c;
                }
            }

            for (int i = 1; i <= N; i++)
                Console.WriteLine(color[i]);
        }
    }
}