A surprising constant

Number Theory Level 5

\[\displaystyle K= \left(\prod _{ i=0 }^{ { p }^{ 2015 }-1 }{ \binom{{ p }^{ 2015 }-1}{i} } \right) \pmod p \]

Find \(K\), given that \(p\) is a prime and is \(1\) mod \(4\).