\[\frac{\varphi -\pi^{32}}{(\sqrt{\varphi}+\pi^{16})(\sqrt[4]{\varphi}+\pi^8)(\sqrt[8]{\varphi}+\pi^4)(\sqrt[16]{\varphi}+\pi^2)(\sqrt[32]{\varphi}+\pi)}= x\] If \(x\) is given as above, where \(\varphi=\dfrac{1+\sqrt{5}}{2}\) is the golden ratio, then \((x+\pi)^{2016}= (\varphi)^y\).

Find the value of \(y\).

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