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 LuaJIT (2.0.4) (judge verdict: Time Limit Exceeded)

local n, m = io.read("*n", "*n")
local edge = {}
local color = {}
local searched_len = {}
for i = 1, n do
  edge[i] = {}
  color[i] = 0
  searched_len[i] = -1
end
for i = 1, m do
  local a, b = io.read("*n", "*n")
  table.insert(edge[a], b)
  table.insert(edge[b], a)
end
local q = io.read("*n")
local query = {}
for iq = 1, q do
  query[iq] = {io.read("*n", "*n", "*n")}
end
for iq = q, 1, -1 do
  local tasks = {{unpack(query[iq])}}
  while 0 < #tasks do
    local src, d, c = unpack(tasks[#tasks])
    table.remove(tasks)
    if color[src] == 0 then
      color[src] = c
    end
    if 0 < d then
      for i = 1, #edge[src] do
        local dst = edge[src][i]
        if searched_len[dst] < d - 1 then
          table.insert(tasks, {dst, d - 1, c})
        end
      end
    end
  end
end
for i = 1, n do
  print(color[i])
end