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 <iostream>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <cmath>
#include <climits>
#include <vector>
#include <string>
#include <queue>
#include <deque>
#include <list>
#include <stack>
#include <set>
#include <map>
#include <algorithm>

#define int long long
#define MOD7 1000000007
#define MOD9 1000000009

#define rep(i, n) for (int i = 0; i < (n); i++)
#define REP(i, a, n) for (int i = (a); i <= (n); i++)
#define all(a) (a).begin(), (a).end()

using namespace std;

int dx[4] = { 1, 0, -1, 0 };
int dy[4] = { 0, -1, 0, 1 };

int nextInt() {int a; cin >> a; return a;}
char nextChar() {char a; cin >> a; return a;}
double nextDouble() {double a; cin >> a; return a;}
string nextString() {string a; cin >> a; return a;}

template<class T> void inputVector(vector<T>& v, int n) {
    v.resize(n);
    for (int i = 0; i < v.size(); i++) cin >> v[i];
}

class Node {
public:
	vector<int> next;
	int color;
	Node() {
		color = 0;
	};
};

class Info {
public:
	int node;
	int color;
	int left;
	Info() {}
	Info(int n, int c, int l) {
		node = n;
		color = c;
		left = l;
	}
};

signed main() {
	int N, M;
	cin >> N >> M;

	vector<int> a(M), b(M);
	rep(i, M) {
		cin >> a[i] >> b[i];
		a[i]--; b[i]--;
	}

	int Q;
	cin >> Q;
	vector<int> v(Q), d(Q), c(Q);
	rep(i, Q) {
		cin >> v[i] >> d[i] >> c[i];
		v[i]--;
	}

	if (N > 2000 || M > 2000 || Q > 2000) return 0;

	vector<Node> node(N);
	rep(i, M) {
		node[a[i]].next.push_back(b[i]);
		node[b[i]].next.push_back(a[i]);
	}

	bool visit[2010];
	rep(i, Q) {
		memset(visit, false, sizeof(visit));
		queue<Info> q;
		q.push(Info(v[i], c[i], d[i]));
		visit[v[i]] = true;
		while (!q.empty()) {
			Info info = q.front(); q.pop();
			node[info.node].color = c[i];
			if (info.left == 0) continue;
			rep(j, node[info.node].next.size()) {
				int nt = node[info.node].next[j];
				if (visit[nt]) continue;
				q.push(Info(nt, c[i], info.left - 1));
			}
		}
	}

	rep(i, N) {
		cout << node[i].color << endl;
	}

    return 0;
}