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<iostream>
#include<vector>
#include<cstring>
#include<queue>
#include<algorithm>
#include<string>
#include<cstdio>
#include<cstdlib>
#include <clocale>
#include<cmath>
#include<sstream>
#include<set>
#include<stack>
using namespace std;
const int INF=0x3f3f3f3f;
const int MX=1e5+10;
typedef unsigned long long ull;
typedef pair<int ,int> p; 
vector<int>vc[MX];
int col[MX],vis[MX];
void dfs(int d,int v,int c){
	if(d==0)return;
	for(int i=0;i<vc[v].size();i++)
		if(!vis[vc[v][i]]){
		vis[vc[v][i]]=1;
		col[vc[v][i]]=c;
		dfs(d-1,vc[v][i],c);
		}
}
int main(){
	int n,m,a,b,q,d,v,c;
	cin>>n>>m;
	memset(col,0,sizeof(col));
	while(m--){
		cin>>a>>b;
		vc[a].push_back(b);
		vc[b].push_back(a);
	}
	cin>>q;
	while(q--){
		memset(vis,0,sizeof(vis));
		cin>>v>>d>>c;
		vis[v]=1;
		col[v]=c;
		dfs(d,v,c);
	}
	for(int i=1;i<=n;i++)
		printf("%d\n",col[i]);
    system("pause");
    return 0;
}