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>
#include<stdlib.h>

typedef struct directedGraph{
  int *vertex;
  int *next;
  int *start;
  int v,e;
  int pointer;
} graph;

graph* newGraph(const int v,const int e){
  graph *g=(graph *)malloc(sizeof(graph));
  g->vertex=(int *)calloc(e,sizeof(int));
  g->next=(int *)calloc(e,sizeof(int));
  g->start=(int *)calloc(v,sizeof(int));
  for(int i=0;i<v;i++) g->start[i]=-1;
  g->v=v;
  g->e=e;
  g->pointer=0;
  return g;
}

void freeGraph(graph *g){
  free(g->vertex);
  free(g->next);
  free(g->start);
  free(g);
  return;
}

void addEdge(graph *g,const int from,const int to){
  const int p=g->pointer;
  g->vertex[p]=to;
  g->next[p]=g->start[from];
  g->start[from]=p;
  g->pointer++;
  return;
}

typedef struct splaNode{
  int v;
  int d;
  int c;
} node;

void run(void){
  int n,m;
  scanf("%d%d",&n,&m);
  graph *g=newGraph(n,2*m);
  while(m--){
    int a,b;
    scanf("%d%d",&a,&b);
    a--;b--;
    addEdge(g,a,b);
    addEdge(g,b,a);
  }
  int q;
  scanf("%d",&q);
  node *s=(node *)calloc(n,sizeof(node));
  int i;
  for(i=0;i<q;i++){
    int v,d,c;
    scanf("%d%d%d",&v,&d,&c);
    s[i]=(node){v-1,d,c};
  }
  int *ans=(int *)calloc(n,sizeof(int));
  int *rad=(int *)calloc(n,sizeof(int));
  for(i=0;i<n;i++) rad[i]=-1;
  node *que=(node *)calloc(n,sizeof(node));
  for(i=q-1;i>=0;i--){
    if(rad[s[i].v]>=s[i].d) continue;
    rad[s[i].v]=s[i].d;
    int front=0;
    int last=0;
    que[last++]=s[i];
    while(front<last){
      const node t=que[front++];
      if(ans[t.v]==0) ans[t.v]=t.c;
      for(int p=g->start[t.v];p!=-1;p=g->next[p]){
	int u=g->vertex[p];
	if(rad[u]>=t.d-1) continue;
	que[last++]=(node){u,t.d-1,t.c};
      }
    }
  }
  for(i=0;i<n;i++) printf("%d\n",ans[i]);
}

int main(void){
  run();
  return 0;
}