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 Perl (v5.18.2) (judge verdict: Wrong Answer)

my @data =<STDIN>;
foreach(@data) { chomp; }
my @num = split(/ /, $data[0]);
my $pn = $num[0];
my $en = $num[1];

my @result;
for(1..$pn) { push(@result, 0); }

my @edge;
for(1..$en) {
	my @ele = split(/ /, $data[$_]);
	push(@edge, "$ele[0],$ele[1]");
	push(@edge, "$ele[1],$ele[0]");
}

my $cn = $data[$en+1];

for(1..$cn) {
	my @ele = split(/ /, $data[$en+1+$_]);
	my $sp = $ele[0];
	my $d = $ele[1];
	my $c = $ele[2];

	color($sp, $d, $c);
}


for(@result) {
	print $_, "\n";
}

sub color {
	my ($s, $d, $c) = @_;

	$result[$s-1]= $c;

	print $s, "-", $d, "-", $c, "\n";
	if($d <= 0) {
		return;
	}
	print "cont\n";

	for(@edge) {
		if($_ =~ /$s,(\d+)/) {
			color($1, $d-1, $c);
		}
	}
}