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 Ruby (2.3.3) (judge verdict: Runtime Error)

h, w = gets.split.map(&:to_i)
n = gets.to_i
color_num = gets.split.map(&:to_i)

field = Array.new(h) {Array.new(w, 0)}

find = ->{
  h.times do |y|
    w.times {|x| return [x, y] if field[y][x].zero?}
  end
  nil
}

num = nil

paint = ->(x, y, color) {
  num -= 1
  return if num < 0
  field[y][x] = color
  [[0, -1], [-1, 0], [1, 0], [0, 1]].each do |dx, dy|
    x1 = x + dx
    y1 = y + dy
    next if x1 < 0 || x1 >= w || y1 < 0 || y1 >= h
    next if field[y1][x1].nonzero?
    paint.(x1, y1, color)
  end
}

n.times do |i|
  x, y = find.()
  num = color_num[i]
  paint.(x, y, i + 1)
end

puts field.map {|row| row.join(" ")}