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: Runtime Error)

#include <iostream>
#include <algorithm>
#include <cassert>
#include <deque>
#include <fstream>
#include <map>
#include <math.h>
#include <memory>
#include <queue>
#include <sstream>
#include <stdio.h>
#include <string>
#include <vector>
#include <bitset>

#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define REP(i,n)  FOR(i,0,n)
#define POW(n) ((n)*(n))
#define ALL(a) (a).begin(),(a).end()
#define dump(v) (cerr << #v << ": " << v << endl)
#define cerr if(true) cerr

using namespace std;

typedef long long ll;
typedef unsigned long long ull;

typedef vector<int> vi;
typedef vector<double> vd;
typedef vector<string> vs;
typedef vector<unsigned long long> vull;

// ll n = to_T<ll>("114514")
template <class T> T to_T(const string& s) { istringstream is(s); T res; is >> res; return res; }
template <class T> string to_s(const T& a) { ostringstream os; os << a; return os.str(); }

int cost[2010][2010];
ll ans[2010];
std::vector<int> E[2010];

void solve(long long N, long long M, vector<long long> a, vector<long long> b, long long Q, vector<long long> v, vector<long long> d, vector<long long> c){
	REP(i,N) REP (j,N) cost[i][j] = 1 << 20;
	REP(i,N) cost[i][i] = 0;

	REP(i,M)
		cost[a[i]][b[i]] = cost[b[i]][a[i]] = 1;

	REP(k, N) REP(i, N) REP(j, N) {
    cost[i][j] = min(cost[i][j], cost[i][k] + cost[k][j]);
  }

	REP(i,N) REP(j,N) if(cost[i][j] != (1 << 20)){
		E[i].push_back(j);
	}

	// REP(i,Q) REP(j,N) if(cost[v[i]][j] <= d[i]){
	// 	ans[j] = c[i];
	// }

	REP(i,Q){
		// if(E[v[i]].empty())continue;
		for(int to : E[v[i]]) if(cost[v[i]][to] <= d[i]){
			ans[to] = c[i];
		}
	}


	REP(i,N)
		cout << ans[i] << endl;
	// REP(i,N){
	// 	cout << "1->" << (i+1) << " " <<cost[0][i]<< endl;
	// }
}



int main(){
	ios::sync_with_stdio(false);
	long long N;
	long long M;
	long long Q;
	cin >> N;
	cin >> M;
	vector<long long> a(M-1+1);
	vector<long long> b(M-1+1);
	for(int i = 0 ; i <= M-1 ; i++){
		cin >> a[i];a[i]--;
		cin >> b[i];b[i]--;
	}
	cin >> Q;
	vector<long long> v(Q-1+1);
	vector<long long> d(Q-1+1);
	vector<long long> c(Q-1+1);
	for(int i = 0 ; i <= Q-1 ; i++){
		cin >> v[i];v[i]--;
		cin >> d[i];
		cin >> c[i];
	}
	solve(N, M, a, b, Q, v, d, c);
	return 0;
}