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;
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); }

        class Solver
        {
            private readonly int[] colors;
            private readonly List<int>[] paths;
            private readonly HashSet<Tuple<int, int>> set;
            public Solver(int N, int[][] edges)
            {
                colors = new int[N];
                paths = new List<int>[N];
                for (int i = 0; i < N; ++i)
                {
                    paths[i] = new List<int>();
                }
                foreach (var edge in edges)
                {
                    int a = edge[0] - 1;
                    int b = edge[1] - 1;
                    paths[a].Add(b);
                    paths[b].Add(a);
                }
                set = new HashSet<Tuple<int, int>>();
            }
            private void Paint(int v, int d, int c)
            {
                var key = new Tuple<int, int>(v, d);
                if (!set.Contains(key))
                {
                    if (d == 0)
                    {
                        colors[v] = c;
                    }
                    else
                    {
                        Paint(v, d - 1, c);
                        foreach (int u in paths[v])
                        {
                            Paint(u, d - 1, c);
                        }
                    }
                    set.Add(key);
                }
            }
            public IEnumerable<int> Solve(int[][] queries)
            {
                foreach (var q in queries.Reverse())
                {
                    int v = q[0] - 1;
                    int d = q[1];
                    int c = q[2];
                    Paint(v, d, c);
                }
                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 new Solver(N, edges).Solve(queries))
            {
                Console.WriteLine(ans);
            }
        }
    }
}