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<cstdio>
const int maxn = 100500;
int head[maxn], d[maxn], v[maxn], c[maxn], pri[maxn], f[maxn];
int n, m, q, x, y, tot;
struct Edge {
	int u, v, next;
} e[maxn];
void add_edge(int u, int v) {
	 e[++tot] = (Edge){u, v, head[u]};
	 head[u] = tot;
}
void dfs(int u, int fa, int dis, int col) {
	if(dis < f[u] || dis < 0) return;
	if(!pri[u]) {
		pri[u] = col;
		f[u] = dis;
	} 
	for(int i = head[u]; i; i = e[i].next) {
		int v = e[i].v;
		if(v == fa) continue;
		dfs(v, u, dis-1, col);
	}
}
int main() {
	scanf("%d%d", &n, &m);
	for(int i = 1; i <= m; i++) {
		scanf("%d%d", &x, &y);
		add_edge(x, y);
		add_edge(y, x);
	}
	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], 0, d[i], c[i]);
	for(int i = 1; i <= n; i++) printf("%d\n", pri[i]);
	return 0;
}