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D - Grid Coloring

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

• $1 ≤ H, W ≤ 100$
• $1 ≤ N ≤ H W$
• $a_i ≥ 1$
• $a_1 + a_2 + ... + a_N = H W$

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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.

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2 2
3
2 1 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.

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3 5
5
1 2 3 4 5

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

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1 1
1
1

1