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 = STDIN.gets.split.map(&:to_i)
hens = []
m.times { hens << STDIN.gets.split.map(&:to_i) }
q = STDIN.gets.to_i
moves = []
q.times { moves << STDIN.gets.split.map(&:to_i) }

tree = Hash.new { [] }
hens.each do |a, b|
  work = (tree[a] || []) + [b]
  tree[a] = work.uniq
  work = (tree[b] || []) + [a]
  tree[b] = work.uniq
end

color = {}
cache = {}
moves.reverse.each do |v, d, c|
  next if cache[[v, d]]
  cache[[v, d]] = true
  target = [v]
  color[v] = c unless color.key?(v)
  d.times do |i|
    dd = d - (i + 1)
    target = tree.values_at(*target).flatten.uniq
    target.each do |t|
      next if cache[[t, dd]]
      cache[[t, dd]] = true
      color[t] = c unless color.key?(t)
    end
  end
end

n.times do |i|
  puts color[i + 1] || 0
end