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: Wrong Answer)

#include <bits/stdc++.h>

#define int long long

using namespace std;

int a[100001];
vector <int> g[100001];
int d[100001];
int c[100001];
int ans[100001];
int was[100001];
int u[100001];
int timer;

void dfs (int v, int k, int col) {
	if (!ans[v]) ans[v] = col;
	u[v] = timer;
	was[v] = max (was[v], k);
	for (auto to : g[v]) {
		if (u[to] == timer) continue;	
		if (was[to] <= k - 1)
			dfs (to, k - 1, col);
	}
}

 main () {
	int n, k = 0;
	int m;
	cin >> n >> m;
	for (int i = 1;i <= m;i ++) {
		int x, y;
		cin >> x >> y;
		g[x].push_back (y);
		g[y].push_back (x);
	}
	int q;
	cin >> q;
	for (int i = 1;i <= q;i ++) {
		cin >> a[i] >> d[i] >> c[i];
	}
	for (int i = q;i >= 1;i --) {
		timer ++;
		dfs (a[i], d[i], c[i]);
	}
	for (int i = 1;i <= n;i ++) cout << ans[i] << endl;
	return 0;
}