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++14 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

/**
 * code generated by JHelper
 * More info: https://github.com/AlexeyDmitriev/JHelper
 * @author Yulian
 */

#include <iostream>
#include <iostream>
#include <fstream>
#include <vector>
#include <set>
#include <cmath>
#include <queue>
#include <deque>
#include <string>
#include <algorithm>
#include <map>


#include <iostream>

#include <fstream>
#include <vector>
#include <set>
#include <cmath>
#include <queue>
#include <deque>
#include <string>
#include <algorithm>
#include <map>



#include <assert.h>


using namespace std;

class B {
public:

  void solve(std::istream &in, std::ostream &out) {
    ios::sync_with_stdio(false);
    int n, m, q, a, b, v, c, d, curr;
    in >> n >> m;
    vector<pair<int, vector<int>>> g(n);
    for (int i = 0; i < m; ++i) {
      in >> a >> b;
      g[a - 1].second.push_back(b - 1);
      g[b - 1].second.push_back(a - 1);
    }
    in >> q;
    vector<bool> visited(n);
    queue<int> cq, nq;
    for (int i = 0; i < q; ++i) {
      cq = queue<int>();
      nq = cq;
      visited = vector<bool>(n);
      in >> v >> d >> c;
      --v;
      cq.push(v);
      for (int j = 0; j <= d && !cq.empty(); ++j) {
        while (!cq.empty()) {
          curr = cq.front();
          cq.pop();
          visited[curr] = true;
          g[curr].first = c;
          for (const auto &el: g[curr].second) {
            if (!visited[el]) {
              nq.push(el);
            }
          }
        }
        cq.swap(nq);
        nq = queue<int>();
      }
    }
    for (int i = 0; i < n; ++i) {
      out << g[i].first << "\n";
    }
    out.flush();
  }
};


int main() {
	B solver;
	std::istream& in(std::cin);
	std::ostream& out(std::cout);
	solver.solve(in, out);
	return 0;
}