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<cstdio>
#include<algorithm>
using namespace std;
#define MAXN 100010
int Adj[MAXN],V[MAXN*2],nxt[MAXN*2],c;
void AddEdge(int u,int v)
{
	c++;V[c]=v,nxt[c]=Adj[u];Adj[u]=c;
}
int vis[MAXN],st[MAXN],col[MAXN],dis[MAXN],cnt;
void BFS(int s,int d,int C)
{
	dis[s]=0,col[s]=C,vis[s]=cnt;
	int l=0,r=0;
	st[r++]=s;
	while(l<r)
	{
		int u=st[l++];
		if(dis[u]==d) continue;
		for(int i=Adj[u];i;i=nxt[i])
			if(vis[V[i]]!=cnt)
			{
				vis[V[i]]=cnt;
				dis[V[i]]=dis[u]+1;
				col[V[i]]=C;
				st[r++]=V[i];
			}
	}
}
int n,m;
int main()
{
	scanf("%d%d",&n,&m);
	int u,v,d,C;
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d",&u,&v);
		AddEdge(u,v);
		AddEdge(v,u);
	}
	scanf("%d",&cnt);
	while(cnt)
	{
		scanf("%d%d%d",&v,&d,&C);
		BFS(v,d,C);
		cnt--;
	}
	for(int i=1;i<=n;i++)
		printf("%d\n",col[i]);
}