# Abnormally Normal

Calculus Level 3

Consider the graph plotted by the equation

$k^x+y^k+x^x=x^k+k^y+y^y$

where $$x>0$$, $$y>0$$, and $$k \in \mathbb{R^+}$$ is a constant.

Let $$G_{k,t}$$ be the gradient of the normal to a curve of the graph at the point $$(t,t)$$ where $$t \in \mathbb{Z^+}$$, $$t \geq k$$ is a real positive integer. Determine the value of

$\prod_{k=2}^{2016} \left( \prod_{t=k}^{k+2015} G_{k,t} \right)$

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