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 <algorithm>
#include <cfloat>
#include <climits>
#include <cmath>
#include <complex>
#include <cstdio>
#include <cstdlib>
#include <cstring>
#include <functional>
#include <iostream>
#include <map>
#include <memory>
#include <queue>
#include <set>
#include <sstream>
#include <stack>
#include <string>
#include <utility>
#include <vector>

using namespace std;

typedef long long ll;

#define sz size()
#define pb push_back
#define mp make_pair
#define fi first
#define se second
#define all(c) (c).begin(), (c).end()
#define rep(i,a,b) for(ll i=(a);i<(b);++i)
#define per(i,a,b) for(ll i=(b-1);i>=(a);--i)
#define clr(a, b) memset((a), (b) ,sizeof(a))
#define ctos(c) string(1,c)
#define print(x) cout<<#x<<" = "<<x<<endl;

#define MOD 1000000007

vector<vector<ll> > vv;
ll d[2020];
ll dd[2020];

void f(int p, int b, int c, int t){
	d[p] = c;
	dd[p] = 1;
	if(t+1<=b){
		rep(i,0,vv[p].sz){
			if(dd[vv[p][i]]==1)continue;
			f(vv[p][i],b,c,t+1);
		}
	}
}

int main(){
	ll n,m;
	cin>>n>>m;
	if(n>2000)return 0;
	if(m>2000)return 0;
	vector<vector<ll> > vv_(n,vector<ll>());
	vv = vv_;
	rep(i,0,m){
		ll a,b;
		cin>>a>>b;
		a--;b--;
		vv[a].pb(b);
		vv[b].pb(a);
	}
	clr(d,0);
	ll q;
	cin>>q;
	if(q>2000)return 0;
	rep(i,0,q){
		ll a,b,c;
		cin>>a>>b>>c;
		a--;
		clr(dd,0);
		f(a,b,c,0);
	}
	rep(i,0,n){
		cout << d[i] << endl;
	}
	return 0;
}