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)

#pragma GCC optimize(3)
#include<bits/stdc++.h>
using namespace std;
const int N=100005;
int co[N],res[N],dis[N],qu[N],qq[N][3],n,m,q,a,b,c,d,v;
vector<int>g[N];
int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		scanf("%d%d",&a,&b);
		g[a].push_back(b);
		g[b].push_back(a);
	}
	scanf("%d",&q);
	for(int i=1;i<=q;i++)	
		for(int j=0;j<3;j++)
			scanf("%d",&qq[q-i+1][j]);
	for(int i=1;i<=q;i++)
	{
		memset(dis,-1,sizeof(dis));
		v=qq[i][0],d=qq[i][1],c=qq[i][2];
		int b=0,e=1;
		qu[0]=v;
		dis[v]=0;
		while(b<e)
		{
			int k=qu[b];
			b++;
			if(dis[k]>d)
				break;
			if(d-dis[k]<res[k])
				continue;
			if(!co[k])
				co[k]=c; 
			res[k]=d-dis[k];
			for(int i=0;i<g[k].size();i++)
			{
				if(dis[g[k][i]]==-1)
				{
					dis[g[k][i]]=dis[k]+1;
					qu[e]=g[k][i];
					e++;
				}
			}
		}
	} 
	for(int i=1;i<=n;i++)
		printf("%d\n",co[i]);
	return 0;
}