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: Accepted)

#include<bits/stdc++.h>
using namespace std;
const int maxn=1e5+10;
int n,m,K;
int Col[maxn];
int Mx[maxn];
inline int Read(){
	register int ch,a;
	while(ch=getchar(),ch<'0'||ch>'9');a=(ch^48);
	while(ch=getchar(),ch>='0'&&ch<='9')a=(a*10)+(ch^48);
	return a;
}

int h[maxn];
struct Edge{
	int to,nxt;
}e[maxn<<1];int tot_Edge;
inline void AddEdge(int from,int to){
	e[++tot_Edge]=(Edge){to,h[from]};
	h[from]=tot_Edge;
}
inline void dfs(int u,int Rem,int col){
	if(!Col[u])Col[u]=col;
	if(Rem<=Mx[u])return;
	Mx[u]=Rem;
	for(int i=h[u];i;i=e[i].nxt)dfs(e[i].to,Rem-1,col);
}

struct Que{
	int u,d,c;
}q[maxn];

int main(){
	n=Read(),m=Read();
	for(int i=1,u,v;i<=m;i++){
		u=Read(),v=Read();
		AddEdge(u,v),AddEdge(v,u);
	}
	K=Read();
	for(int i=1;i<=K;i++){
		q[i].u=Read(),q[i].d=Read(),q[i].c=Read();
	}
	for(int i=K;i>=1;i--)dfs(q[i].u,q[i].d,q[i].c);
	for(int i=1;i<=n;i++)printf("%d\n",Col[i]);puts("");
	return 0;
}