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++14 (GCC 5.4.1) (judge verdict: Wrong Answer)

#include<iostream>
#include<cstdio>
#include<cstdlib>
#include<cmath>
#include<cstring>
using namespace std;

const int N=1e5+10;


int n,m,q;

int last[N],nx[N<<1],to[N<<1],tot;
int d[N],c[N],v[N];
int vis[N],us[N];

void Add(int x,int y)
{
	tot++;
	to[tot]=y;
	nx[tot]=last[x];
	last[x]=tot;
}

void dfs(int x,int C,int dep,int lim)
{
	if(dep>lim) return;
	if(vis[x]&&lim-dep<=us[x]) return;
	if(!vis[x]) vis[x]=C;
	us[x]=max(us[x],lim-dep);
	for(int j=last[x];j;j=nx[j])
		dfs(to[j],C,dep+1,lim);
}


int main()
{
	scanf("%d%d",&n,&m);
	for(int i=1;i<=m;i++)
	{
		int x,y;
		scanf("%d%d",&x,&y);
		Add(x,y);
		Add(y,x);
	}
	scanf("%d",&q);
	for(int i=1;i<=q;i++) scanf("%d%d%d",&v[i],&d[i],&c[i]);
	for(int i=q;i;i--)
		if(d[i]>us[v[i]]) dfs(v[i],c[i],0,d[i]);
	for(int i=1;i<=n;i++) printf("%d\n",vis[i]);
	return 0;
}