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 <vector>
#include <queue>
#define REP(i, a, n) for(int i = (a); i <= (n); i++)
using namespace std;

int color[100001];
vector<int> E[100001];

void dfs(int v, int d, int c, int last) {
  color[v] = c;

  for(int j = 0; j < E[v].size(); j++) {
    if(E[v][j] != last && d > 0) {
      dfs(E[v][j], d - 1, c, v);
    }
  }
}

int main(void) {
  int N, M; cin >> N >> M;
  if(N > 2000 || M > 2000) return 0;
  REP(i, 1, M) {
    int a, b; cin >> a >> b;
    E[a].push_back(b);
    E[b].push_back(a);
  }

  REP(i, 1, N) color[i] = 0;

  int Q; cin >> Q;
  if(Q > 2000) return 0;
  REP(i, 1, Q) {
    int v, d, c; cin >> v >> d >> c;
    dfs(v, d, c, 0);
  }

  REP(i, 1, N) cout << color[i] << endl;

  return 0;
}