Contest Duration: - (local time) (100 minutes) Back to Home
D - Grid Coloring /

Time Limit: 2 sec / Memory Limit: 256 MB

### 問題文

H 行、横 W 列のマス目があります。 すぬけ君は、このマス目を色 1, 2, ..., N で塗り分けようとしています。 このとき、次の条件が成り立つようにします。

• i (1 ≤ i ≤ N) について、色 i のマスはちょうど a_i 個存在する。 ただし、a_1 + a_2 + ... + a_N = H W である。
• i (1 ≤ i ≤ N) について、色 i のマスは上下左右に連結である。 すなわち、どの色 i のマスからどの色 i のマスへも、上下左右に隣り合う色 i のマスのみを辿って行き来できる。

### 制約

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

### 入力

H W
N
a_1 a_2 ... a_N


### 出力

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


### 入力例 1

2 2
3
2 1 1


### 出力例 1

1 1
2 3


1 2
3 1


### 入力例 2

3 5
5
1 2 3 4 5


### 出力例 2

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


### 入力例 3

1 1
1
1


### 出力例 3

1


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