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") 
#define TASK ""
#pragma GCC target("sse,sse2,sse3,ssse3,sse4,popcnt,abm,mmx") 
#define __USE_MINGW_ANSI_STDIO 0
#include<bits/stdc++.h>                               
using namespace std;

#define PI acos(-1)
#define pb push_back
#define fi first
#define se second
#define sz(a) (int)(a).size()
#define all(c) (c).begin(), (c).end()
#define TIMESTAMP fprintf(stderr, "Execution time: %.3lf s.\n", (double)clock()/CLOCKS_PER_SEC)

typedef long long ll;
typedef long double ld;
typedef vector<int> vi;
typedef vector<ll> vll;
typedef pair <int, int> pii;
typedef vector <vi> vvi;
typedef vector <pii> vpii;
typedef vector<string> vs;

const int MAXN = 1e5 + 9;
const int MOD = (int)(1e9 + 7);
const int INF = 100500;

int n, m, q;
vvi gg;
int col[MAXN];
bool used[MAXN];

void input() {
	cin >> n >> m;
	gg.resize(n);
	for(int i = 0; i < m; i++) {
		int a, b;
		cin >> a >> b;
		a--, b--;
		gg[a].pb(b);
		gg[b].pb(a);
	}
}

void dfs(int v, int color, int depth) {
	used[v] = 1;
	col[v] = color;
	if(depth == 0) return;
	for(auto to : gg[v]) {
		if(!used[to]) {
			dfs(to, color, depth - 1);
		}
	}
}

void solve() {
	cin >> q;
	for(int i = 0; i < q; i++) {
		int v, d, c;
		cin >> v >> d >> c;
		v--;
		memset(used, 0, sizeof(used));
		dfs(v, c, d);
	}
	for(int i = 0; i < n; i++) cout << col[i] << endl;
}

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