Problem Description

Index gives you a function as follows:

Draw its graph (where * means the graph passes through that point, and . means it does not) on a grid of size $n \times m$, where the range of $x$ is $[0,n-1]$ and the range of $f(x)$ is $[0,m-1]$.

Specifically, you need to output an $n \times m$ character matrix. If the function passes through an integer point $(x,y)$, then output * at the position that is the $(x+1)$-th column from left to right and the $(y+1)$-th row from bottom to top; otherwise output ..

Input Format

The first line contains three integers $n,m,k$.

The second line contains $k+1$ integers, where the $i$-th integer represents $a_{i-1}$.

Output Format

Output a total of $m$ lines, each containing $n$ characters, which is the graph of the function. Specifically, output * at the position that is the $(x+1)$-th column from left to right and the $(y+1)$-th row from bottom to top if and only if the function passes through $(x,y)$; otherwise output ..

5 5 1
0 1

....*
...*.
..*..
.*...
*....

8 8 1
0 2

........
...*....
........
..*.....
........
.*......
........
*.......

Hint

Explanation for Sample $1$:

The function is $f(x)=x$. Obviously, when $x\in[0,4], f(x)\in[0,4]$, it passes through the integer points $(0,0),(1,1),(2,2),(3,3),(4,4)$.

For $100\%$ of the testdata, $-12\le a_i\le 12$ and $n=m$. Each test point is equally weighted.

Translated by ChatGPT 5