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 Ruby (2.3.3) (judge verdict: Wrong Answer)

def solve(c,adj,color)
	color[c[0]]=c[2]
	dfs(c[0],c[1],c[2],adj,color)
end

def dfs(pt,d,co,adj,color)
	if d>0 && adj[pt].length>0
		for nx in adj[pt]
			if color[nx]!=co
				color[nx]=co
				dfs(nx,d-1,co,adj,color)
			end
		end
	end
end

if __FILE__==$0
	rl_i=lambda{|str,dl|str.strip.split(dl).map(&:to_i)}
	r_i=lambda{|str|str.strip.to_i}
	n,m=rl_i[gets," "]
	color=Array.new(n){0}
	adj=Array.new(n){[]}
	m.times do |i|
		e=rl_i[gets," "].map do |x| x-1 end
		adj[e[0]].push(e[1])
		adj[e[1]].push(e[0])
	end
	q=r_i[gets]
	q.times do |i|
		c=rl_i[gets," "]
		c[0]-=1
		solve(c,adj,color)
	end
        color.each do |co| p co end
end