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.Linq;
using System.Collections.Generic;

public class Program
{
    public static void Main()
    {
        var nm = Console.ReadLine().Split()
            .Select(x => int.Parse(x))
            .ToArray();
        var n = nm[0];
        var m = nm[1];
        var adlQuery =
            from i in Enumerable.Range(1, m)
            let vu = Console.ReadLine().Split()
                .Select(x => int.Parse(x) - 1)
                .OrderBy(x => x)
                .ToArray()
            select vu into es
            from e in new[] { es, es.Reverse() }
            let v = e.First()
            let u = e.Last()
            orderby u ascending
            group u by v into g
            orderby g.Key ascending
            select g;
        var adl = adlQuery.ToDictionary(x => x.Key);
        var q = int.Parse(Console.ReadLine());
        var queriesQuery =
            from i in Enumerable.Range(1, q)
            let x = Console.ReadLine().Split()
                .Select(x => int.Parse(x))
                .ToArray()
            select new { i, v = x[0] - 1, d = x[1], c = x[2] };
        var queries = queriesQuery.ToArray();
        var map = Enumerable.Concat(new[] { 0 }, queries.Select(x => x.c)).ToArray();

        var finalVertices = queries
            .Reverse()
            .Aggregate(
                new int[n, 2], 
                (dp, x) => Splat(dp, new[] { x.v }, x.d, x.i, adl), 
                dp => Enumerable.Range(0, n).Select(i => map[dp[i, 0]])
            );
        foreach (var v in finalVertices)
        {
            Console.WriteLine(v);
        }
    }

    static int[,] Splat(int[,] dp, int[] vertices, int d, int q, Dictionary<int, IGrouping<int, int>> adl)
    {
        if (!vertices.Any() || d < 0)
        {
            return dp;
        }

        var bfsQuery =
            from v in vertices
            where dp[v, 1] < d
            join adjs in adl on v equals adjs.Key into ts
            from t in ts
            from u in t.Value
            group u by u into g
            select g.Key;
        var bfs = bfsQuery.ToArray();
        
        foreach (var v in vertices)
        {
            if (dp[v, 0] <= q)
            {
                dp[v, 0] = q;
            }

            if (dp[v, 1] < d)
            {
                dp[v, 1] = d;
            }
        }

        return Splat(dp, bfs, d - 1, q, adl);
    }
}