AT_past202306_c 円の描画

On a two-dimensional plane, there is a circle of radius $ R $ centered at point $ (X, Y) $ . For an integer pair $ (i, j) $ , let us define $ S_{i,j} = $ `#` if point $ (i, j) $ is in the interior or on the circumference of the circle, and $ S_{i,j} = $ `.` otherwise. Print $ S_{i,j} $ for all integer pairs $ (i, j) $ such that $ -N \leq i,j \leq N $ .

The input is given from Standard Input in the following format: > $ X $ $ Y $ $ R $ $ N $

Print $ (2N+1) $ lines. The $ i $ -th line should contain $ S_{i-N-1,-N}, S_{i-N-1,-N+1}, \ldots, S_{i-N-1,N-1} $ , and $ S_{i-N-1,N} $ in this order, separated by spaces.

### Sample Explanation 1 On a two-dimensional plane, there is a circle of radius $ 1 $ centered at point $ (1,-2) $ . We have $ S_{i,j} = $ `#` if $ (i,j) $ is one of $ (0,-2),(1,-3),(1,-2),(1,-1) $ , and $ (2,-2) $ , and $ S_{i,j} = $ `.` otherwise. ### Constraints - $ -100 \leq X, Y \leq 100 $ - $ 1 \leq R \leq 100 $ - $ 1 \leq N \leq 200 $ - If $ S_{i,j} = $ `#`, then $ -N \leq i,j \leq N $ . - All values in the input are integers.