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: Time Limit Exceeded)

N, M = gets.split(/ /).collect{|num| num.to_i}

$e_table = []

$d_table = []
$queue = []
(1..N).each{|i|
	$e_table[i] = []
	$d_table[i] = []
	$d_table[i][i] = 0
	$queue << [i, i]
}

M.times{
	a, b = gets.split(/ /).collect{|num| num.to_i}
	$e_table[a] << b
	$e_table[b] << a
}

def update(i, j)
	d = $d_table[i][j] + 1
	if d > 10
		return
	end
	$e_table[i].each{|v|
		if (d2 = $d_table[j][v]) == nil || d2 > d
			$d_table[j][v] = d
			$d_table[v][j] = d
			$queue << [j, v]
		end
	}
end

while pair = $queue.pop
	i, j = pair
	
	update(i, j)
	update(j, i)
end


#(1..N).each{|i|
#	(1..N).each{|j|
#		print "#{$d_table[i][j]} "
#	}
#	puts $d_table[i].collect{|x| x == nil ? "-" : x}.join(" ")
#}

Q = gets.to_i

c_list = []
(1..N).each{|i|
	c_list[i] = 0
}

Q.times{
	v, d, c = gets.split(/ /).collect{|num| num.to_i}
	
	d_list = $d_table[v]
	(1..N).each{|i|
		if (d2 = d_list[i]) != nil && d2 <= d
			c_list[i] = c
		end
	}
}

(1..N).each{|i|
	puts c_list[i]
}