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: Time Limit Exceeded)

using System;
using System.IO;
using System.Linq;
using System.Collections;
using System.Collections.Generic;
using System.Numerics;
using System.Diagnostics;
using System.Text;
using System.Text.RegularExpressions;
using System.Threading.Tasks;
using static System.Math;
using MethodImplOptions = System.Runtime.CompilerServices.MethodImplOptions;
using MethodImplAttribute = System.Runtime.CompilerServices.MethodImplAttribute;
using System.Runtime.CompilerServices;


static class P
{
    static void Main()
    {


        var nm = Console.ReadLine().Split().Select(int.Parse).ToList();
        var edges = Enumerable.Repeat(0, nm[1]).Select(_ => Console.ReadLine().Split().Select(x => int.Parse(x) - 1).ToList()).ToList();
        var q = int.Parse(Console.ReadLine());
        //ある点の現在の色
        Tuple<int, int>[] currentColor = Enumerable.Repeat(0, nm[0]).Select(_ => new Tuple<int, int>(0,-1)).ToArray();
        //Tuple<int, int>[][] colors = Enumerable.Repeat(0, nm[0]).Select(_ => Enumerable.Repeat(0,11).Select(__ => new Tuple<int, int>(0, -1)).ToArray()).ToArray();
        Tuple<int, int>[][] colors = new Tuple<int, int>[nm[0]][];
        Tuple<int, int>[][] nextColors = new Tuple<int, int>[nm[0]][];
        for (int i = 0; i < nm[0]; i++)
        {
            colors[i] = new Tuple<int, int>[11];
            nextColors[i] = new Tuple<int, int>[11];
            for (int j = 0; j < 11; j++) colors[i][j] = new Tuple<int, int>(0, -1);
        }
        //ある点が保持している距離ごとの最も新しい色
        for (int i = 0; i < q; i++)
        {
            var vdc = Console.ReadLine().Split().Select(int.Parse).ToList();
            currentColor[vdc[0] - 1] = new Tuple<int, int>(vdc[2], i);
            colors[vdc[0] - 1][vdc[1]] = new Tuple<int, int>(vdc[2], i);
        }
        for (int i = 1; i <= 10; i++)
        {
            for (int j = 0; j < nm[0]; j++)
                for (int k = 0; k < 11; k++) nextColors[j][k] = new Tuple<int, int>(0, -1);

            for (int index = 0; index < nm[1]; index++)
            {
                var edge = edges[index];
                for (int j = 0; j < 11 - i; j++)
                {
                    nextColors[edge[0]][j] = nextColors[edge[0]][j].Item2 > colors[edge[1]][j + 1].Item2 ? nextColors[edge[0]][j] : colors[edge[1]][j + 1];
                    nextColors[edge[1]][j] = nextColors[edge[1]][j].Item2 > colors[edge[0]][j + 1].Item2 ? nextColors[edge[1]][j] : colors[edge[0]][j + 1];
                }
            }

            var tmp = colors;
            colors = nextColors;
            nextColors = tmp;

            for (int j = 0; j < nm[0]; j++)
            {
                var currentNewest = new Tuple<int, int>(0, -1);
                for (int k = 0; k < 11 - i; k++)
                {
                    if (currentNewest.Item2 < colors[j][k].Item2) currentNewest = colors[j][k];
                }

                if(currentColor[j].Item2 < currentNewest.Item2) currentColor[j] = currentNewest;
            }
        }
        Console.WriteLine(string.Join("\n", currentColor.Select(x => x.Item1)));
    }
}