Plotting a Polynomial Function

Given a polynomial function defined as

$$f(x)=a_kx^k+a_{k-1}x^{k-1}+\cdots+a_1x+a_0,$$

draw its graph on an n × m grid. The x-coordinate ranges over [0, n-1] and the y-coordinate (i.e. the value of f(x)) must lie in the range [0, m-1].

For each integer x in [0, n-1], if the computed f(x) is an integer within [0, m-1], mark that grid cell with a *. Otherwise, leave it as .. The grid is printed such that columns correspond to x-values from left (x = 0) to right (x = n-1), and rows correspond to y-values from bottom (y = 0) to top (y = m-1).

inputFormat

The input consists of two lines:

• The first line contains three integers: n, m, and k separated by spaces. Here, n and m represent the dimensions of the grid, and k is the degree of the polynomial.
• The second line contains k+1 integers: ak ak-1 ... a0, which are the coefficients of the polynomial.

The polynomial is defined as:

$$f(x)=a_kx^k+a_{k-1}x^{k-1}+\cdots+a_1x+a_0.$$

Only integer values of x in the range [0, n-1] are considered.

outputFormat

Output the grid as m lines, each consisting of n characters. The grid represents a coordinate system where the leftmost column corresponds to x = 0 and the rightmost to x = n-1, and the bottom row corresponds to y = 0 while the top row corresponds to y = m-1.

For each integer x, if f(x) is an integer within [0, m-1], mark the cell at column (x+1) (from left) and row (f(x)+1) (from bottom) with a *; otherwise, the cell should contain a ..

sample

10 10 2
1 0 0

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

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