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: Accepted)

H,W=gets.split.map &:to_i
N=gets.to_i
a=gets.split.map &:to_i

c=Array.new(H+2){Array.new(W+2){0}}
(H+2).times{|i| c[i][0]=c[i][-1]=-1}
(W+2).times{|j| c[0][j]=c[-1][j]=-1}

dy=[1,0,-1,0]
dx=[0,1,0,-1]
d=0
n=1
y,x=0,1
until a.empty?
  ny=y+dy[d%4]
  nx=x+dx[d%4]
  next d+=1 if c[ny][nx]!=0
  y=ny
  x=nx
  c[y][x]=n
  a[0]-=1
  if a[0].zero?
    n+=1
    a.shift
  end
end

puts c[1..H].map{|i|i[1..W]*" "}