Problem:
Score : 400 points

Problem Statement

We have a grid with H rows and W columns of squares.
Snuke is painting these squares in colors 1, 2, ..., N.
Here, the following conditions should be satisfied:

For each i (1 ≤ i ≤ N), there are exactly a_i squares painted in Color i. Here, a_1 + a_2 + ... + a_N = H W.

For each i (1 ≤ i ≤ N), the squares painted in Color i are 4-connected. That is, every square painted in Color i can be reached from every square painted in Color i by repeatedly traveling to a horizontally or vertically adjacent square painted in Color i.

Find a way to paint the squares so that the conditions are satisfied.
It can be shown that a solution always exists.

Constraints

1 ≤ H, W ≤ 100

1 ≤ N ≤ H W

a_i ≥ 1

a_1 + a_2 + ... + a_N = H W

Input

Input is given from Standard Input in the following format:

H W
N
a_1 a_2 ... a_N

Output

Print one way to paint the squares that satisfies the conditions.
Output in the following format:

c_{1 1} ... c_{1 W}
:
c_{H 1} ... c_{H W}

Here, c_{i j} is the color of the square at the i-th row from the top and j-th column from the left.

Sample Input 1

2 2
3
2 1 1

Sample Output 1

1 1
2 3

Below is an example of an invalid solution:

1 2
3 1

This is because the squares painted in Color 1 are not 4-connected.

Sample Input 2

3 5
5
1 2 3 4 5

Sample Output 2

1 4 4 4 3
2 5 4 5 3
2 5 5 5 3

Sample Input 3

1 1
1
1

Sample Output 3

1

Solution in OCaml (4.02.3) (judge verdict: Runtime Error)

let rec foldn f a = function
  | 0 -> a
  | n -> foldn f (f a) (n - 1)

let () =
  let h, w = Scanf.scanf "%d %d\n" (fun h w -> h, w) in
  let n = Scanf.scanf "%d\n" (fun n -> n) in
  let as_ = Array.init n (fun i -> Scanf.scanf "%d " (fun a -> (i + 1, a))) in
  Array.fold_left (fun (acc, current, current_sum) (i, a) ->
    let c = Char.chr (i + Char.code '0') in
    if w <= current_sum + a then
      foldn (fun xs -> [String.make w c] :: xs)
        ((String.make (w - current_sum) c :: current) :: acc)
        ((current_sum + a) / w - 1), [String.make ((current_sum + a - w) mod w) c], (current_sum + a - w) mod w
    else (acc, String.make a c :: current, a + current_sum)) ([], [], 0) as_
  |> (fun (acc, _, _) -> acc)
  |> List.fold_left (fun (acc, b) a -> ((if b then List.rev a else a) :: acc, not b)) ([], true)
  |> fst
  |> List.map (String.concat "")
  |> List.iter print_endline