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: Wrong Answer)

#include <iostream>
#include <string>
#include <vector>
#include <utility>
#include <map>
#include <algorithm>

using namespace std;

void trace(
  const vector<vector<int>>& vertices,
  vector<int>& colors,
  int old_v,
  int v,
  int d,
  int c
) {
  // cerr << "trace: " << (old_v+1) << ", " << (v+1) << ", " << d << ", " << c << endl;
  colors[v] = c;
  if (d <= 0) return;
  for (auto next_v: vertices[v]) {
    if (colors[next_v] == c) continue;
    trace(vertices, colors, v, next_v, d - 1, c);
  }
}

void paint(
  const vector<vector<int>>& vertices,
  vector<int>& colors,
  int v,
  int d,
  int c
) {
  // cerr << "paint: " << (v+1) << ", " << d << ", " << c << endl;
  trace(vertices, colors, v, v, d, c);
}

int main()
{
  int N, M;
  cin >> N >> M;
  vector<vector<int>> vertices(N);
  vector<int> colors(N, 0);
  for (int i = 0; i < M; ++i) {
    int a, b;
    cin >> a >> b;
    --a; --b;
    vertices[a].push_back(b);
    vertices[b].push_back(a);
  }

  int Q;
  cin >> Q;
  for (int i = 0; i < Q; ++i) {
    int v, d, c;
    cin >> v >> d >> c;
    --v;
    paint(vertices, colors, v, d, c);
  }

  for (auto c: colors) cout << c << endl;
  return 0;
}