A surprising constant

K=(i=0p20151(p20151i))(modp)\displaystyle K= \left(\prod _{ i=0 }^{ { p }^{ 2015 }-1 }{ \binom{{ p }^{ 2015 }-1}{i} } \right) \pmod p

Find KK, given that pp is a prime and is 11 mod 44.

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