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: Time Limit Exceeded)

#include<bits/stdc++.h>
#define mp make_pair
#define pb push_back
using namespace std;
typedef long long ll;
typedef unsigned long long ull;
typedef vector<int > vi;
typedef pair<int ,int > pii;
typedef vector<pii> vii;
const int inf=0x3f3f3f3f, maxn=100007, mod=1e9+7;
const ll linf=0x3f3f3f3f3f3f3f3fLL;
int n,m;
vi e1[maxn];
vii e2[maxn];
int Q;
int v[maxn],dd[maxn],c[maxn];
int cc[maxn];
bool vis[maxn];
int main(){
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++){
		int x,y;
		scanf("%d%d",&x,&y);
		e1[x].pb(y);
		e1[y].pb(x);
	}
	for(int i=1;i<=n;i++){
		queue<pii > q;
		while(!q.empty())q.pop();
		q.push(mp(i,0));
		while(!q.empty()){
			pii top=q.front();
			q.pop();
			int u=top.first,d=top.second;
			if(d>10){
				break;
			}
			e2[i].pb(mp(u,d));
			for(int j=0;j<e1[u].size();j++){
				q.push(mp(e1[u][j],d+1));
			}
		} 
	}
	scanf("%d",&Q);
	for(int i=1;i<=Q;i++){
		scanf("%d%d%d",&v[i],&dd[i],&c[i]);
	}
	for(int i=Q;i>=1;i--){
		for(int j=0;j<e2[v[i]].size();j++){
			if(e2[v[i]][j].second<=dd[i]&&!vis[e2[v[i]][j].first]){
				cc[e2[v[i]][j].first]=c[i];
				vis[e2[v[i]][j].first]=true;
			}
		}
	}
	for(int i=1;i<=n;i++){
		printf("%d\n",cc[i]);
	}
	return 0;
}