Painters Painting Circles

Algebra Level 5

A group of $$x$$ painters split up into $$y\ (\le x)$$ groups of not necessarily the same size to work on a project of painting circles on the wall. Each painter is given just enough paint to fill in 4 square meters of any shape.

Now, if each group uses their total amount of paint to fill in a largest circle possible, and the sum of the circumferences of all these circles is at most $$k \sqrt{xy}$$ meters with $$k$$ a positive real number, what is $$\big\lfloor k^2 \big\rfloor?$$

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