1555. All Squares

Geometrically, any square has a unique, well-defined centre point. On a grid this is only true if the sides of the square are an odd number of points long. Since any odd number can be written in the form 2k+1, we can characterise any such square by specifying k, that is we can say that a square whose sides are of length 2k+1 has size k. Now define a pattern of squares as follows.

The largest square is of size k (that is sides are of length 2k+1) and is centred in a grid of size 1024 (that is the grid sides are of length 2049).

The smallest permissible square is of size 1 and the largest is of size 512, thus 1<=k<=512 .

All squares of size k > 1 have a square of size k div 2 centred on each of their 4 corners. (Div implies integer division, thus 9 div 2 = 4).

The top left corner of the screen has coordinates (0,0), the bottom right has coordinates (2048, 2048).

Hence, given a value of k, we can draw a unique pattern of squares according to the above rules. Furthermore any point on the screen will be surrounded by zero or more squares. (If the point is on the border of a square, it is considered to be surrounded by that square). Thus if the size of the largest square is given as 15, then the following pattern would be produced.

Write a program that will read in a value of k and the coordinates of a point, and will determine how many squares surround the point.