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: Time Limit Exceeded)

#include <stdio.h>
#include <stdlib.h>
typedef struct gp {
  int c;
  int n;
  int *a;
} GP;

GP *g;

void saiki(int v, int d, int c)
{
  if(d<0) return;
  g[v].c = c;
  int i;
  for(i=0; i<g[v].n; i++){
    saiki(g[v].a[i], d-1, c);
  }
  return;
}

main()
{
  int n,m,q, i,j,k, a,b,v,d,c;
  scanf("%d%d", &n, &m);
  g = (GP *)malloc(sizeof(GP) * n);
  for(i=0; i<n; i++){
    g[i].a = (int *)malloc(sizeof(int) * (n-1));
    g[i].c=0;
    g[i].n=0;
  }

  for(i=0; i<m; i++){
    scanf("%d%d", &a, &b);
    a--;
    b--;
    g[a].a[g[a].n] = b;
    g[b].a[g[b].n] = a;
    g[a].n++;
    g[b].n++;
  }

  scanf("%d", &q);
  for(k=0; k<q; k++){
    scanf("%d%d%d", &v, &d, &c);
    saiki(v-1,d,c);
  }

  for(i=0; i<n; i++){
    printf("%d\n", g[i].c);
  }
  return 0;
}