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: Accepted)

#include <cstdio>
#include <cstring>
#include <cassert>
#include <algorithm>
#include <iostream>
#include <vector>

using namespace std;

#define TRACE(x) cerr << #x << " = " << x << endl
#define REP(i, n) for (int i=0; i<n; i++)
#define FOR(i, a, b) for (int i=(a); i<(b); i++)
#define _ << " " <<

typedef long long ll;
typedef pair<int, int> P;
#define X first
#define Y second

const int MAXN = 1<<17, MAXD = 12;

int bio[MAXN];
vector <int> V[MAXN];
int rje[MAXN];
int v[MAXN], d[MAXN], c[MAXN];

void dfs(int node, int dist, int col)
{
  if (dist < 0) return;
  if (bio[node] == -1) rje[node] = col;
  if (bio[node] >= dist) return;
  bio[node] = dist;
  
  for (auto it : V[node])
    dfs(it, dist-1, col);
}

int main()
{
  int n, m;
  scanf("%d%d", &n, &m);

  REP(i, m) {
    int a, b;
    scanf("%d%d", &a, &b); a--; b--;
    V[a].push_back(b);
    V[b].push_back(a);
  }

  int brq;
  scanf("%d", &brq);

  for (int i=brq-1; i>=0; i--) {
    scanf("%d%d%d", &v[i], &d[i], &c[i]); v[i]--;
  }

  memset(bio, -1, sizeof bio);

  REP(i, brq)
    dfs(v[i], d[i], c[i]);

  REP(i, n) printf("%d\n", rje[i]);

  return 0;
}