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)

//#pragma GCC optimize("O3") 
//#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx") 
//#define __USE_MINGW_ANSI_STDIO 0
#include <bits/stdc++.h>
#define TASK "zak"
#define pb push_back
#define fi first
#define se second
using namespace std;

#ifdef LOCAL
	#define eprintf(...) fprintf(stderr, __VA_ARGS__)
#else
	#define eprintf(...) (void)42
#endif

// every true-boy doesn't read statement!

typedef long long ll;
typedef pair < int, int > pii;
typedef pair < ll, ll > pll;
typedef long double ld;

const int MAXN = (int)2e5 + 22;

int N, M, Q;
vector < vector < int > > gg;
int cc[MAXN], dd[MAXN];

void bfs(int s, int d, int c) {
	queue < int > qq;
	//if (!cc[s]) {
		qq.push(s);
		cc[s] = c;
		dd[s] = 0;
	//}
	while (!qq.empty()) {
		int v = qq.front();
		int ds = dd[v];
		qq.pop();
		for (auto to : gg[v]) {
			// !cc[to]
			if (ds + 1 <= d) {
				cc[to] = c;
				dd[to] = ds + 1;
				qq.push(to);
			}
		}	
	}
}

void solve() {
	cin >> N >> M;
	gg.resize(N);
	int u, v;
	for (int i = 0; i < M; i++) {
		cin >> u >> v;
		--u, --v;
		gg[u].pb(v);
		gg[v].pb(u);	
	}
	cin >> Q;
	vector < pair < pii, int > > qq;
	int d, c;
	for (int i = 0; i < Q; i++) {
		cin >> v >> d >> c;
		--v;
		bfs(v, d, c);
		//qq.pb({ { v, d }, c }); 
	}
	/*while (!qq.empty()) {
		v = qq.back().fi.fi;
		d = qq.back().fi.se;
		c = qq.back().se;
		qq.pop_back();
		bfs(v, d, c);
	}*/
	for (int i = 0; i < N; i++)
		cout << cc[i] << "\n";
}

int main() {
	ios_base::sync_with_stdio(0);
	cin.tie(0);
#ifdef LOCAL
	assert(freopen("xxx.in", "r", stdin));
	assert(freopen("xxx.out", "w", stdout));
#else
	//assert(freopen(TASK".in", "r", stdin));
	//assert(freopen(TASK".out", "w", stdout));
#endif
	solve();
	return 0;
}