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)

//此程序使用了qt专属名称，请勿模仿。侵权必究！！！
//我真是太菜了啊……
#include<bits/stdc++.h>
using namespace std;
#define mp make_pair
#define ll long long
const ll N=100010;
int n,m,q,t=0,f[N];
vector<int> a[N];
bool vis[N];
int v[N],d[N],c[N];
inline int read()
{
	int sum=0,flag=1;
	char c;
	for(;c<'0'||c>'9';c=getchar())if(c=='-') flag=-1;
	for(;c>='0'&&c<='9';c=getchar())sum=(sum<<1)+(sum<<3)+c-'0';
	return sum*flag;
}
inline void dfs(int x,int y,int z)
{
	if(vis[x]>=y||y<=0)
	{
		return;
	}
	vis[x]=y;
	if(!f[x])
	{
		f[x]=z;
	}
	for(int i=a[x].size()-1;i>=0;--i)
	{
		dfs(a[x][i],y-1,z);
	}
}
int main()
{
	n=read();
	m=read();
	for(int i=1;i<=m;++i)
	{
		int x=read(),y=read();
		a[x].push_back(y);
		a[y].push_back(x);
	}
	q=read();
	for(int i=1;i<=q;++i)
	{
		v[i]=read();
		d[i]=read()+1;
		c[i]=read();
	}
	for(int i=q;i;--i)
	{
		dfs(v[i],d[i],c[i]);
	}
	for(int i=1;i<=n;++i)
	{
		printf("%d\n",f[i]);
	}
	return 0;
}