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: Time Limit Exceeded)

#include <bits/stdc++.h>
using namespace std;

#define ALL(a) begin(a), end(a)
#define SZ(a) ((int)(a).size())

#ifdef __DEBUG
#define debug if (true)
#else
#define debug if (false)
#endif

typedef long long ll;
typedef pair<int, int> pii;
typedef vector<int> vi;

#define fixed asldkjasld

const int N = 1e5 + 5;

struct Query {
  int v, d, c;
};

int n, m, q;
int c[N];
bool fixed[N];
vector<pii> g[N];
vi maxDist[N];
Query qs[N];
map<int, int> pos[N];

int main() {
  ios::sync_with_stdio(false);
  cin.tie(nullptr);
  scanf("%d%d", &n, &m);
  for (int i = 0; i < m; i++) {
    int u, v;
    scanf("%d%d", &u, &v);
    u--; v--;
    g[u].push_back(pii(v, -1));
    g[v].push_back(pii(u, -1));
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < SZ(g[i]); j++) {
      int to = g[i][j].first;
      pos[i][to] = j;
    }
  }
  for (int i = 0; i < n; i++) {
    for (int j = 0; j < SZ(g[i]); j++) {
      int to = g[i][j].first;
      g[i][j].second = pos[to][i];
    }
  }
  scanf("%d", &q);
  for (int i = 0; i < q; i++) {
    int v, d, c;
    scanf("%d%d%d", &v, &d, &c);
    v--;
    qs[i] = {v, d, c};
  }
  for (int i = 0; i < n; i++) {
    maxDist[i].assign(SZ(g[i]) + 1, -1);
  }
  for (int i = q - 1; i >= 0; i--) {
    int start, d, newC;
    start = qs[i].v;
    d = qs[i].d;
    newC = qs[i].c;
    if (maxDist[start][SZ(g[start])] >= d) {
      continue;
    }
    queue<pii> q;
    q.push(pii(start, SZ(g[start])));
    maxDist[start][SZ(g[start])] = d;
    while (!q.empty()) {
      int u = q.front().first;
      int from = q.front().second;
      if (!fixed[u]) {
        fixed[u] = true;
        c[u] = newC;
      }
      q.pop();
      int nxt = maxDist[u][from] - 1;
      for (const auto &it : g[u]) {
        if (maxDist[it.first][it.second] < nxt) {
          maxDist[it.first][it.second] = nxt;
          q.push(pii(it.first, it.second));
        }
      }
    }
  }
  for (int i = 0; i < n; i++) {
    printf("%d\n", c[i]);
  }
  return 0;
}