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 (GCC 5.4.1) (judge verdict: Runtime Error)

#include<stdio.h>
 
void paint(int n,int g[],int w[2048][2048],int nv,int ld,int nd,int c,int hc[],int st[]){
	int i;
	if(nd <= ld && st[nv] > nd){
		g[nv] = c;
		st[nv] = nd;
		for(i = 1;i <= hc[nv];i++){
			paint(n,g,w,w[nv][i],ld,nd+1,c,hc,st);
		}
	}
}
 
int main(void){
	int i,j,n,m,a,b,w[2048][2048]={0},hc[2048]={0},q,v,d,c,nc[2048]={0},st[2048];
	scanf("%d%d",&n,&m);
	for(i = 1;i <= m;i++){
		scanf("%d%d",&a,&b);
		hc[a]++;hc[b]++;
		w[a][hc[a]] = b;
		w[b][hc[b]] = a;
	}
	scanf("%d",&q);
	for(i = 1;i <= q;i++){
		scanf("%d%d%d",&v,&d,&c);
		if(d >= 2000){d = 2000;}
		for(j = 1;j <= n;j++){st[j] = 114514;}
		paint(n,nc,w,v,d,0,c,hc,st);
	}
	for(i = 1;i <= n;i++){printf("%d\n",nc[i]);}
	return 0;
}