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: Accepted)

N, M = gets.split.map(&:to_i)
edges = Array.new(N){Hash.new}
M.times do
    a, b = gets.split.map(&:to_i)
    edges[a-1][b-1] = true
    edges[b-1][a-1] = true
end
Q = gets.to_i
vs, ds, cs = [], [], []
Q.times do |i|
    vs[i], ds[i], cs[i] = gets.split.map(&:to_i)
    vs[i] -= 1
end

ans = Array.new(N, 0)
width = Array.new(N, -1)
(Q-1).downto(0) do |q|
    v, d, c = vs[q], ds[q], cs[q]
    next if width[v] >= d
    ans[v] = c if ans[v] == 0
    width[v] = d
    updated = [v]
    (d-1).downto(0) do |i|
        nup = []
        updated.each do |src|
            edges[src].each do |dst, _|
                next if width[dst] >= i
                ans[dst] = c if ans[dst] == 0
                width[dst] = i
                nup.push(dst)
            end
        end
        break if nup.length == 0
        updated = nup
    end
end

puts ans