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 <bits/stdc++.h>
using namespace std;
#define REP(i,n) for(int i = 0; i < (int)(n); ++i)
#define DEBUG(x) cerr << #x << " = " << x << endl
const int INF = (int)1e9;
struct Edge {
  int to;
  Edge(int to_) : to(to_) { }
};
struct State {
  int pos, cost;
  State(int pos_, int cost_) : pos(pos_), cost(cost_) { }
};
vector<int> shortest_path(const vector<vector<Edge>> &G, const int src) {
  const int n = G.size();
  vector<int> d(n, INF);
  queue<State> Q;
  Q.emplace(src, 0);
  d[src] = 0;
  while(!Q.empty()) {
    State s = Q.front(); Q.pop();
    if(s.cost > d[s.pos]) continue;
    for(Edge e : G[s.pos]) {
      if(d[e.to] > s.cost + 1) {
        d[e.to] = s.cost + 1;
        Q.emplace(e.to, d[e.to]);
      }
    }
  }
  return d;
}
int main() {
  int N, M; cin >> N >> M;
  vector<vector<Edge>> G(N);
  REP(i,M) {
    int a, b; cin >> a >> b;
    a--; b--;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  int Q; cin >> Q;
  vector<int> V(Q), D(Q), C(Q);
  REP(i,Q) {
    cin >> V[i] >> D[i] >> C[i];
    V[i]--;
  }
  if(N <= 2000 && M <= 2000 && Q <= 2000) {
    reverse(V.begin(), V.end());
    reverse(D.begin(), D.end());
    reverse(C.begin(), C.end());
    REP(i,N) {
      int ans = 0;
      vector<int> d = shortest_path(G, i);
      REP(j,Q) {
        if(d[V[j]] <= D[j]) {
          ans = C[j];
          break;
        }
      }
      cout << ans << endl;
    }
  }
}