For nonzero real numbers x and y, define x \circ y=\frac{x y}{x+y}. Compute
2^{1} \circ\left(2^{2} \circ\left(2^{3} \circ \cdots \circ\left(2^{2016} \circ 2^{2017}\right)\right)\right)
For nonzero real numbers x and y, define x \circ y=\frac{x y}{x+y}. Compute