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: Runtime Error)

#include <iostream>
#include <stdio.h>
#include <string>
#include <vector>
#include <cmath>
#include <algorithm>

using namespace std;

int N,M,Q;
void paint(int v, int d, int c, vector<vector <int> >&A, vector<int> &C)
{
  C[v-1] = c;
  if(d == 0) return;
  for(int j=0; j < N; j++){
    if(A[v-1][j] == 1 && C[j] == 0){
      C[j] = c;
      paint(j+1,d-1,c,A,C);
    }
  }
}

int main()
{
  cin >> N >> M;
  vector<vector <int> >A(N,vector<int>(N));
  vector<int>C(N);
  for(int i=0; i < N; i++)
    C[i] = 0;
  int a,b;
  for(int i=0; i < M; i++){
    cin >> a >> b;
    A[a-1][b-1] = 1;
    A[b-1][a-1] = 1;
  }
  cin >> Q;
  vector<int>V(Q);
  vector<int>D(Q);
  vector<int>CC(Q);
  for(int i=0; i < Q; i++){
    cin >> V[i] >> D[i] >> CC[i];
  }
  for(int i= Q-1; i >= 0; i--){
    paint(V[i],D[i],CC[i],A,C);
  }
  for(int i=0; i < N; i++)
    cout << C[i] << endl;
  return 0;
}