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;
using System.Linq;

namespace AGC012
{
    public class B
    {
        private void Run()
        {
            var input = Console.ReadLine().Trim().Split();
            var N = int.Parse(input[0]);
            var M = int.Parse(input[1]);

            var edges = Enumerable.Range(0, N).Select(_ => new List<int>()).ToArray();

            while (M-- > 0)
            {
                input = Console.ReadLine().Trim().Split();
                var a = int.Parse(input[0]) - 1;
                var b = int.Parse(input[1]) - 1;
                edges[a].Add(b);
                edges[b].Add(a);
            }

            var Q = int.Parse(Console.ReadLine().Trim());
            var queries = new List<Tuple<int, int, int>>();
            while (Q-- > 0)
            {
                input = Console.ReadLine().Trim().Split();
                var v = int.Parse(input[0]) - 1;
                var d = int.Parse(input[1]);
                var c = int.Parse(input[2]);
                queries.Add(Tuple.Create(v, d, c));
            }

            var color = new int[N];
            var maxUsedDistance = new int[N];
            foreach (var query in queries.AsEnumerable().Reverse())
            {
                var v = query.Item1;
                var d = query.Item2;
                var c = query.Item3;

                var q = new Queue<Tuple<int, int>>();
                q.Enqueue(Tuple.Create(v, d));
                while (q.Count > 0)
                {
                    var t = q.Dequeue();
                    var index = t.Item1;
                    var rest = t.Item2;

                    if (color[index] == 0) { color[index] = c; }
                    if (rest == 0) { continue; }
                    if (maxUsedDistance[index] >= rest) { continue; }
                    maxUsedDistance[index] = rest;

                    foreach (var edge in edges[index])
                    {
                        if (maxUsedDistance[edge] > rest - 1) { continue; }
                        q.Enqueue(Tuple.Create(edge, rest - 1));
                    }
                }
            }
            Console.WriteLine(string.Join(Environment.NewLine, color));
        }

        public static void Main()
        {
            var old = Console.Out;
            using (var writer = new System.IO.StreamWriter(Console.OpenStandardOutput()) { AutoFlush = false })
            {
                Console.SetOut(writer);
                new B().Run();
                Console.Out.Flush();
                Console.SetOut(old);
            }
        }
    }
}