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;

const int INF = 1 << 30;

int N, M, Q;
vector< int > g[100000];
int a[100000], b[100000], c[100000];
int color[100000], dist[100000];

int main()
{
  cin >> N >> M;
  while(M--) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  cin >> Q;
  for(int i = 0; i < Q; i++) {
    cin >> a[i] >> b[i] >> c[i];
    --a[i];
  }

  memset(color, -1, sizeof(color));
  memset(dist, -1, sizeof(dist));
  priority_queue< tuple< int, int, int > > que;
  for(int i = 0; i < Q; i++) {
    que.emplace(i, a[i], b[i]);
    color[a[i]] = i;
    dist[a[i]] = b[i];
  }

  while(!que.empty()) {
    int idx, depth, num;
    tie(num, idx, depth) = que.top();
    que.pop();
    if(depth > 0) {
      for(auto &to : g[idx]) {
        if(color[to] < num) color[to] = num;
        if(dist[to] < depth - 1) {
          dist[to] = depth - 1;
          que.emplace(num, to, depth - 1);
        }
      }
    }
  }

  for(int i = 0; i < N; i++) {
    if(~color[i]) cout << c[color[i]] << endl;
    else cout << 0 << endl;
  }
}