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
            select g;
        var adl = Enumerable.Range(0, n)
            .GroupJoin(adlQuery, i => i, adj => adj.Key, (_, inner) => inner.SelectMany(adj => adj.ToArray()))
            .DefaultIfEmpty()
            .ToArray();
        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 dp = Enumerable.Range(1, 3).Select(_ => new int[n]).ToArray();
        foreach (var query in queries.Reverse())
        {
            var vs = new[] { query.v };
            for (int d = query.d; d > -1; --d)
            {
                var bfs = vs
                    .Where(v => dp[1][v] < d)
                    .SelectMany(v => adl[v])
                    .Distinct()
                    .ToArray();
                foreach (var v in vs)
                {
                    if (dp[0][v] <= query.i)
                    {
                        dp[0][v] = query.i;
                        dp[2][v] = query.c;
                    }

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

        foreach (var v in dp[2])
        {
            Console.WriteLine(v);
        }
    }
}