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.Collections.Generic;

public class Program
{
    private int N, M;
    private int[] A, B;
    private int Q;
    private int[] V, D, C;
    private int[,] Dp;
    private List<int>[] Edge;

    public void Solve()
    {
        var sc = new Scanner();

        N = sc.NextInt();
        M = sc.NextInt();
        A = new int[M];
        B = new int[M];
        for (int i = 0; i < M; i++)
        {
            A[i] = sc.NextInt() - 1;
            B[i] = sc.NextInt() - 1;
        }

        Q = sc.NextInt();

        V = new int[Q];
        D = new int[Q];
        C = new int[Q];

        for (int i = 0; i < Q; i++)
        {
            V[i] = sc.NextInt() - 1;
            D[i] = sc.NextInt();
            C[i] = sc.NextInt();
        }

        Edge = new List<int>[N];
        for (int i = 0; i < N; i++)
        {
            Edge[i] = new List<int>();
        }

        for (int i = 0; i < M; i++)
        {
            Edge[A[i]].Add(B[i]);
            Edge[B[i]].Add(A[i]);
        }

        Dp = new int[N, 11];

        for (int i = Q - 1; i >= 0; i--)
        {
            Search(V[i], D[i], i + 1);
        }

        int[] ans = new int[N];
        for (int i = 0; i < N; i++)
        {
            int max = 0;
            for (int j = 0; j <=10; j++)
            {
                max = Math.Max(Dp[i, j], max);
            }

            if (max != 0)
            {
                ans[i] = C[max-1];
            }
        }
        
        Console.WriteLine(string.Join("\n",ans));
    }

    private void Search(int n, int d, int i)
    {
        for (int j = d; j <= 10; j++)
        {
            if (Dp[n, j] != 0)
            {
                return;
            }
        }

        Dp[n, d] = i;

        if (d == 0)
            return;

        foreach (var j in Edge[n])
        {
            Search(j, d - 1, i);
        }
    }

    public static void Main(string[] args)
    {
        new Program().Solve();
    }
}

class Scanner
{
    public Scanner()
    {
        _pos = 0;
        _line = new string[0];
    }

    const char Separator = ' ';
    private int _pos;
    private string[] _line;

    #region スペース区切りで取得

    public string Next()
    {
        if (_pos >= _line.Length)
        {
            _line = Console.ReadLine().Split(Separator);
            _pos = 0;
        }

        return _line[_pos++];
    }

    public int NextInt()
    {
        return int.Parse(Next());
    }

    public long NextLong()
    {
        return long.Parse(Next());
    }

    public double NextDouble()
    {
        return double.Parse(Next());
    }

    #endregion

    #region 型変換

    private int[] ToIntArray(string[] array)
    {
        var result = new int[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = int.Parse(array[i]);
        }

        return result;
    }

    private long[] ToLongArray(string[] array)
    {
        var result = new long[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = long.Parse(array[i]);
        }

        return result;
    }

    private double[] ToDoubleArray(string[] array)
    {
        var result = new double[array.Length];
        for (int i = 0; i < array.Length; i++)
        {
            result[i] = double.Parse(array[i]);
        }

        return result;
    }

    #endregion

    #region 配列取得

    public string[] Array()
    {
        if (_pos >= _line.Length)
            _line = Console.ReadLine().Split(Separator);

        _pos = _line.Length;
        return _line;
    }

    public int[] IntArray()
    {
        return ToIntArray(Array());
    }

    public long[] LongArray()
    {
        return ToLongArray(Array());
    }

    public double[] DoubleArray()
    {
        return ToDoubleArray(Array());
    }

    #endregion
}