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 (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>

typedef struct List{
	struct List* next;
	int value;
} list;

int N, M, Q;
int color[100001];
list edge[100001];

void make_edge(int n1, int n2) {
	list *node, *p = &edge[n1];
	while (p->next != NULL) p = p->next;
	node = malloc(sizeof(list));
	node->next = NULL;
	node->value = n2;
	p->next = node;
}

void print_edge() {
	int i;
	list *p;
	for (i = 1; i <= N; i++) {
		printf("%d:", i);
		p = &edge[i];
		while (p != NULL) {
			printf("%d ", p->value);
			p = p->next;
		}
		printf("\n");
	}
}

void dfs(int v, int d, int c) {
	color[v] = c;
	if (d <= 0) return;

	list *p = edge[v].next;
	while (p != NULL) {
		dfs(p->value, d - 1, c);
		p = p->next;
	}
}

int main(void) {
	int i, a, b, v, d, c;

	scanf("%d%d", &N, &M);
	for (i = 1; i <= N; i++) {
		edge[i].next = NULL;
		edge[i].value = i;
	}
	for (i = 0; i < M; i++) {
		scanf("%d%d", &a, &b);
		make_edge(a, b);
		make_edge(b, a);
	}

	scanf("%d", &Q);
	for (i = 0; i < Q; i++) {
		scanf("%d%d%d", &v, &d, &c);
		dfs(v, d, c);
	}
	
	for (i = 1; i <= N; i++) {
		printf("%d\n", color[i]);
	}
	return 0;
}