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)

io = STDIN
$h,$w=io.gets.split.map(&:to_i)
$n=io.gets.to_i
$a=io.gets.split.map(&:to_i)
$bd=[]
$bd << [:busy]*(2+$w)
$h.times do
  $bd << [:busy] + Array.new($w) + [:busy]
end
$bd << [:busy]*(2+$w)

$cand=[[1,0],[-1,0],[0,1],[0,-1]]
def bfs(c,pos,cnt)
  return true if cnt==0
  x,y=pos
  $cand.each do |xx,yy|
    if $bd[x+xx][y+yy]==nil
      $bd[x+xx][y+yy]=c
      return true if bfs(c,[x+xx,y+yy],cnt-1)
      $bd[x+xx][y+yy]=nil
    end
  end
  return false
end
def empty_search
  (1..$h).each do |i|
    (1..$w).each do |j|
      return [i,j] if $bd[i][j]==nil
    end
  end
  false
end
def search
  queue = $a.sort.reverse.zip($n.downto(1).map).to_a
  while item = queue.shift
    ct,c=item
    i,j=empty_search
    return unless i
    $bd[i][j]=c
    unless bfs(c,[i,j],ct-1)
      $bd[i][j]=nil
      queue.unshift(ct,c)
    end
  end
end
search
(1..$h).each do |i|
  puts $bd[i][1..-2].join(" ")
end