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: Wrong Answer)

#include<cstdio>
#include<fstream>
#include<queue>
#include<iostream>
#include<cstring>
#define N 100010
using namespace std;
int n,m;
struct rode{
  int y,next;
}e[N<<1]={};
int fl[N]={},len=0;
int a[N]={};
inline int read()
{
	int s = 0, w = 1;
	char c = getchar();
	while ((c<'0' || c>'9') && c != '0')c = getchar();
	if (c == '-')w = -1, c = getchar();
	while (c <= '9'&&c >= '0')s = (s << 3) + (s << 1) + c - '0', c = getchar();
	return s * w;
}
inline void inc(int x,int y)
{
  e[++len].y=y;
  e[len].next=fl[x];
  fl[x]=len;
}
struct que{
  int u,d,c;
}qu[N]={};
int c[N]={};
bool vis[N]={};
void dfs(int u,int v,int d,int co)
{
  if(d==0)return ;
  for(int i=fl[u];i;i=e[i].next)
   {
     int vv=e[i].y;
     if(vis[vv])continue;
     if(c[vv]==0)c[vv]=co;
     vis[vv]=1;
     dfs(vv,v,d-1,co);
     vis[vv]=0;
   }
}
int main()
{
  n=read();m=read();
  // for(int i=1;i<=n;++i)a[i]=read(),c[i]=0;
  for(int i=1;i<=m;++i)
  {
    int x=read(),y=read();
    inc(x,y);inc(y,x);
  }
  int q=read();
  for(int i=1;i<=q;++i)qu[i].u=read(),qu[i].d=read(),qu[i].c=read();//,printf("%d %d %d\n",qu[i].u,qu[i].d,qu[i].c);
  for(int i=q;i>=1;--i)
  {
    int u=qu[i].u,d=qu[i].d,co=qu[i].c;
    if(c[u]==0)c[u]=co,vis[u]=1,dfs(u,u,d,co);
  }
  for(int i=1;i<=n;++i)printf("%d\n",c[i]);
  return 0;
}