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 OCaml (4.02.3) (judge verdict: Accepted)

let fst3 (a,b,c) = a
let () = Scanf.scanf "%d %d" @@ fun n m ->
  let es = Array.init m (fun _ -> Scanf.scanf " %d %d" @@ fun a b -> a-1, b-1) in
  Scanf.scanf " %d" @@ fun q ->

  let qa =
    let t = Array.init 11 (fun _ -> []) in
    for i = 0 to q-1 do
      Scanf.scanf " %d %d %d" @@ fun v d c ->
      t.(10-d) <- (i, v-1, c) :: t.(10-d)
    done;
    Array.map List.rev t
  in

  let color = Array.make n (-1, 0, -1) in
  qa.(0) |> List.iter (fun (i, v, c) -> color.(v) <- i, c, 0);
  for r = 1 to 10 do
    Array.sort (fun (a,b) (c,d) ->
      min (fst3 color.(a)) (fst3 color.(b)) - min (fst3 color.(c)) (fst3 color.(d))) es;
    Array.iter (fun (u, v) ->
      let iu, cu, ru = color.(u) in
      let iv, cv, rv = color.(v) in
      if iu > iv && ru < r then color.(v) <- (iu, cu, ru+1);
      if iv > iu && rv < r then color.(u) <- (iv, cv, rv+1);
    ) es;
    qa.(r) |> List.iter (fun (i, v, c) ->
      let ia, _, _ = color.(v) in
      if i > ia then color.(v) <- (i, c, r));
  done;

  Array.iter (fun (_, c, _) -> Printf.printf "%d\n" c) color