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"

using namespace std;

int ch[100002][2];

struct Graph {
	vector<int> next;
	int color = 0;
};

int func(int p, vector<Graph>& g, int v, int d, int c) {
	if (ch[v - 1][0] == p && ch[v-1][1] >= v)
		return 0;

	g[v - 1].color = c;
	ch[v - 1][0] = p;
	ch[v - 1][1] = d;

	if (d == 0)
		return 0;

	for (int i = 0; i < g[v - 1].next.size(); i++) {
		func(p, g, g[v - 1].next[i], d - 1, c);
	}

	return 0;
}

int main() {

	int n, m;
	scanf("%d %d", &n, &m);

	vector<Graph> g(n);

	int a, b;
	for (int i = 0; i < m; i++) {
		scanf("%d %d", &a, &b);
		g[a - 1].next.push_back(b);
		g[b - 1].next.push_back(a);
	}

	int q;
	cin >> q;

	int v, d, c;
	for (int i = 0; i < q; i++) {
		scanf("%d %d %d", &v, &d, &c);
		func(i + 1, g, v, d, c);
	}

	for (int i = 0; i < n; i++) {
		printf("%d\n", g[i].color);
	}

	return 0;
}