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.IO;
using System.Globalization;
using System.Diagnostics;
using static System.Console;
using Pair = System.Collections.Generic.KeyValuePair<int, int>;

class Program
{
    static void Main()
    {
        SetOut(new StreamWriter(OpenStandardOutput()) { AutoFlush = false });
        new Program().Solve();
        Out.Flush();
    }
    Scanner cin = new Scanner();
    Random rnd = new Random();
    Stopwatch sw = new Stopwatch();
    readonly int[] dd = { 0, 1, 0, -1, 0 };
    readonly int mod = 1000000007;
    readonly string alfa = "abcdefghijklmnopqrstuvwxyz";

    int N, M;
    int[] color;

    struct Edge : IComparable
    {
        public int to, cost;
        public Edge(int to, int cost)
        {
            this.to = to;
            this.cost = cost;
        }
        public int CompareTo(object obj)
        {
            return cost - ((Edge)obj).cost;
        }
    }
    //List<Edge>[] G;
    List<int>[] H;    

    void Solve()
    {
        N = cin.Nextint;
        M = cin.Nextint;
        //G = Enumerable.Range(0, N).Select(i => new List<Edge>()).ToArray();
        H = Enumerable.Range(0, N).Select(i => new List<int>()).ToArray();

        color = new int[N];

        for (int i = 0; i < M; i++)
        {
            int a = cin.Nextint - 1, b = cin.Nextint - 1;
            //G[a].Add(new Edge(b, 1));
            //G[b].Add(new Edge(a, 1));
            H[a].Add(b);
            H[b].Add(a);
        }
        int Q = cin.Nextint;
        
        for (int i = 0; i < Q; i++)
        {
            int v = cin.Nextint - 1, d = cin.Nextint, c = cin.Nextint;

            var Q1 = new Queue<int>();
            var Q2 = new Queue<int>();
            Q1.Enqueue(v);
            Q2.Enqueue(0);
            var MEMO = new bool[N];
            MEMO[v] = true;
            color[v] = c;

            while (Q1.Any())
            {
                int u = Q1.Dequeue(), depth = Q2.Dequeue();
                if (depth == d) continue;
                foreach (var j in H[u])
                {
                    if (MEMO[j]) continue;
                    Q1.Enqueue(j);
                    Q2.Enqueue(depth + 1);
                    color[j] = c;
                    MEMO[j] = true;
                }
            }          

            
        }



        foreach (var item in color)
        {
            WriteLine(item);
        }
    }
  
}

/*class PriorityQueue<T> where T : IComparable
{
    List<T> heap;
    int size;
    int Compare(T x, T y) { return y.CompareTo(x); }
    public PriorityQueue() { heap = new List<T>(); }

    public void Enqueue(T x)
    {
        heap.Add(x);
        int i = size++;

        while (i > 0)
        {
            int p = (i - 1) >> 1;

            if (Compare(heap[p], x) <= 0) break;

            heap[i] = heap[p];
            i = p;
        }
        heap[i] = x;
    }

    public T Dequeue()
    {
        T ret = heap[0];
        T x = heap[--size];

        int i = 0;
        while ((i << 1) + 1 < size)
        {
            int a = (i << 1) + 1;
            int b = (i << 1) + 2;

            if (b < size && Compare(heap[b], heap[a]) < 0)
                a = b;
            if (Compare(heap[a], x) >= 0)
                break;

            heap[i] = heap[a];
            i = a;
        }
        heap[i] = x;
        heap.RemoveAt(size);
        return ret;
    }

    public int Count { get { return size; } }

    public bool Any() { return size > 0; }

    public T Peek() { return heap[0]; }
}*/

class Scanner
{
    string[] s; int i;
    char[] cs = new char[] { ' ' };
    public Scanner() { s = new string[0]; i = 0; }
    public string[] Scan { get { return ReadLine().Split(); } }
    public int[] Scanint { get { return Array.ConvertAll(Scan, int.Parse); } }
    public long[] Scanlong { get { return Array.ConvertAll(Scan, long.Parse); } }
    public double[] Scandouble { get { return Array.ConvertAll(Scan, double.Parse); } }
    public string Next
    {
        get
        {
            if (i < s.Length) return s[i++];
            string st = ReadLine();
            while (st == "") st = ReadLine();
            s = st.Split(cs, StringSplitOptions.RemoveEmptyEntries);
            i = 0;
            return Next;
        }
    }
    public int Nextint { get { return int.Parse(Next); } }
    public long Nextlong { get { return long.Parse(Next); } }
    public double Nextdouble { get { return double.Parse(Next); } }
}