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 <cstring>
#include <cstdio>
using namespace std;

int head[100005], tot, n, m, q, v[100005], d[100005], c[100005], ou[100005], maxd[100005];
struct edge {
	int to, nxt;
} G[300005];

inline void add(int u, int v) {
	tot++;
	G[tot].to = v;
	G[tot].nxt = head[u];
	head[u] = tot;
}

void dfs(int un, int ds, int c) {
	if(maxd[un] >= ds) return;
	if(!ou[un]) ou[un] = c;
	if(!ds) return;
	maxd[un] = ds;
	for (int i = head[un]; i; i = G[i].nxt) dfs(G[i].to, ds - 1, c);
}

int main() {
	scanf ("%d %d", &n, &m);
	int u, vd;
	for (int i = 1; i <= m; i++) {
		scanf ("%d %d", &u, &vd);
		add(u, vd); add(vd, u);
	}
	memset (maxd, -1, sizeof (maxd));
	scanf ("%d", &q);
	for (int i = 1; i <= q; i++) scanf ("%d %d %d", &v[i], &d[i], &c[i]);
	for (int i = q; i >= 1; i--) dfs(v[i], d[i], c[i]);
	for (int i = 1; i <= n; i++) printf ("%d\n", ou[i]);
	return 0;
}