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.Collections.Generic;
using System.Linq;
using System.Text;

namespace AtCoder
{
    class Program
    {
        private const int MODULO = 1000000007;
        private static string Read() { return Console.ReadLine(); }
        private static int ReadInt() { return int.Parse(Read()); }
        private static long ReadLong() { return long.Parse(Read()); }
        private static double ReadDouble() { return double.Parse(Read()); }
        private static int[] ReadInts() { return Array.ConvertAll(Read().Split(), int.Parse); }
        private static long[] ReadLongs() { return Array.ConvertAll(Read().Split(), long.Parse); }
        private static double[] ReadDoubles() { return Array.ConvertAll(Read().Split(), double.Parse); }

        static IEnumerable<int> Solve(int N, int M, int[][] edges, int Q, int[][] queries)
        {
            var paths = new List<int>[N];
            int[][] memo = new int[N][];
            for (int i = 0; i < N; ++i)
            {
                paths[i] = new List<int>();
                memo[i] = Enumerable.Repeat(int.MaxValue, N).ToArray();
                memo[i][i] = 0;
            }
            foreach (var edge in edges)
            {
                int a = edge[0] - 1;
                int b = edge[1] - 1;
                paths[a].Add(b);
                paths[b].Add(a);
            }
            for (int i = 0; i < N; ++i)
            {
                var q = new Queue<int>();
                q.Enqueue(i);
                while (q.Count > 0)
                {
                    int j = q.Dequeue();
                    foreach (var k in paths[j])
                    {
                        if (memo[i][k] > memo[i][j] + 1)
                        {
                            memo[i][k] = memo[i][j] + 1;
                            q.Enqueue(k);
                        }
                    }
                }
            }
            var colors = new int[N];
            var nodes = Enumerable.Range(0, N).ToList();
            for (int i = Q - 1; i >= 0; --i)
            {
                int v = queries[i][0] - 1;
                int d = queries[i][1];
                int c = queries[i][2];
                nodes.Sort((a, b) => memo[v][a] - memo[v][b]);
                for (int j = 0; j < nodes.Count; ++j)
                {
                    while (j < nodes.Count)
                    {
                        int w = nodes[j];
                        if (memo[v][w] <= d)
                        {
                            colors[w] = c;
                            nodes.RemoveAt(j);
                        }
                        else
                        {
                            j = nodes.Count;
                        }
                    }
                }
            }
            return colors;
        }
        static void Main(string[] args)
        {
            var V = ReadInts();
            var N = V[0];
            var M = V[1];
            var edges = new int[M][];
            for (int i = 0; i < M; ++i) { edges[i] = ReadInts(); }
            var Q = ReadInt();
            var queries = new int[Q][];
            for (int i = 0; i < Q; ++i) { queries[i] = ReadInts(); }
            foreach (int ans in Solve(N, M, edges, Q, queries))
            {
                Console.WriteLine(ans);
            }
        }
    }
}