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 <iostream>
#include <algorithm>
#include <vector>
#include <queue>

using namespace std;
typedef long long int64;
const int kMaxN = 1e5+10;

int n, m, q;
vector<int> G[kMaxN];
int col[kMaxN], pot[kMaxN];
int v[kMaxN], c[kMaxN], maxd[kMaxN];

void bfs(int s, int maxd, int c) {
	queue<int> Q;
	if (maxd > pot[s]) {
		if (col[s] == 0) {
			col[s] = c;
		}
		pot[s] = maxd;
		Q.push(s);
	}

	while (!Q.empty()) {
		int x = Q.front();
		// cout << x << "\n";
		Q.pop();

		for (auto y : G[x]) {
			if (pot[x] - 1 > pot[y]) {
				if (col[y] == 0) {
					col[y] = c;
				}
				pot[y] = pot[x] - 1;
				Q.push(y);
			}
		}
	}
}

void solve() {

	cin >> n >> m;

	for (int i = 1; i <= m; ++i) {
		int a, b;
		cin >> a >> b;
		G[a].push_back(b);
		G[b].push_back(a);
	}

	for (int i = 1; i <= n; ++i) {
		pot[i] = -1;
		col[i] = 0;
	}

	cin >> q;

	for (int i = 1; i <= q; ++i) {
		cin >> v[i] >> maxd[i] >> c[i];
	}

	for (int i = q; i >= 1; --i) {
		// cout << "Here\n";
		bfs(v[i], maxd[i], c[i]);
	}

	for (int i = 1; i <= n; ++i) {
		cout << col[i] << "\n";
	}
	cout << "\n";
}

void reset() {
	for (int i = 1; i <= n; ++i) {
		G[i].clear();
	}
}

int main() {
	int tests = 1;
	for (;tests; --tests) {
		solve();
		reset();
	}
}