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 int int64_t
#define fi first
#define se second
#define endl '\n'
vector<vector<int>> g;
vector<int> color;
map<int, map<int, bool>> was;

void makeItColored(int v, int d, int c) {
     color[v] = c;
     was[v][d] = true;
     if (d == 0) {
          return;
     }
     if (!(was.count(v) && was[v].count(d - 1))) {
          makeItColored(v, d - 1, c);
     }
     for (auto u : g[v]) {
          if (!(was.count(u) && was[u].count(d - 1))) {
               makeItColored(u, d - 1, c);
          }
     }
}

signed main()
{
     srand(time(nullptr));
     ios::sync_with_stdio(false);
     cin.tie(0);
     cout.tie(0);
     int n, m, q;
     cin >> n >> m;
     g.resize(n);
     color.resize(n);
     for (int i = 0; i < m; ++i) {
          int a, b;
          cin >> a >> b;
          a--, b--;
          g[a].push_back(b);
          g[b].push_back(a);
     }
     cin >> q;
     vector<pair<int, pair<int, int>>> qu(q);
     
     for (int qq = 0; qq < q; ++qq) {
          int v, d, c;
          cin >> v >> d >> c;
          v--;
          qu.push_back({v, {d, c}});
     }
     reverse(qu.begin(), qu.end());
     for (int qq = 0; qq < q; ++qq) {
          int v = qu[qq].first;
          int d = qu[qq].second.first;
          int col = qu[qq].second.second;
          makeItColored(v, d, col);
     }
     for (int i = 0; i < n; ++i) {
          cout << color[i] << ' ';
     }
     return 0;
}