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<cstdio>
#include <iostream>
#include<algorithm>
#include<string>
#include<cstring>
#include<queue>
#include<vector>
#include<functional>
#include<cmath>
#include<map>
#include<stack>
#include<cstdlib>
#include<list>
#include<set>
#include<numeric>

using namespace std;
typedef long long ll;
typedef pair<int, int> P;

int N, M, Q;
ll G[2010][2010];
ll color[100010];

int dfs(int v, int d, int c) {
	if (d == 0)return 0;
	for (int i = 0; i <= N; i++) {
		if (G[v][i]) {
			G[v][i] = G[i][v] = 0;
			color[i] = c;
			dfs(i,d-1,c);
			G[v][i] = G[i][v] = 1;
		}
	}
}

int main() {
	cin >> N >> M;
	
	for (int i = 0; i < M; i++) {
		int a, b;
		cin >> a >> b;
		G[a][b] = 1;
		G[b][a] = 1;
	}

	cin >> Q;
	for (int i = 0; i < Q; i++) {
		int v, d, c;
		cin >> v >> d >> c;
		color[v] = c;
		dfs(v, d, c);
	}

	for (int i = 1; i <= N; i++) {
		cout << color[i] << endl;
	}
	return 0;
}