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;

namespace agc012_b
{
    public static class Program
    {
        static void Main()
        {
            int[] x = Console.ReadLine().Split().Select(int.Parse).ToArray();
            x[0]++;
            bool[,] edge = new bool[x[0], x[0]];
            int[] point = new int[x[0]];
            for (int i = 0; i < x[1]; i++)
            {
                int[] a = Console.ReadLine().Split().Select(int.Parse).ToArray();
                edge[a[0], a[1]] = true;
                edge[a[1], a[0]] = true;
            }
            int q = int.Parse(Console.ReadLine());
            for (int i = 0; i < q; i++)
            {
                int[] b = Console.ReadLine().Split().Select(int.Parse).ToArray();
                point[b[0]] = b[2];
                Queue<int> draw = new Queue<int>();
                draw.Enqueue(b[0]);
                draw.Enqueue(-1);
                for (int j = 0; j < b[1];)
                {
                    int now = draw.Dequeue();
                    if (now == -1)
                    {
                        j++;
                        draw.Enqueue(-1);
                    }
                    else
                    {
                        for (int k = 0; k < x[0]; k++)
                        {
                            if (edge[now, k])
                            {
                                point[k] = b[2];
                                draw.Enqueue(k);
                            }
                        }
                    }
                }
            }
            for (int i = 1; i < x[0]; i++)
            {
                Console.WriteLine(point[i]);
            }
        }
    }
}