I'm trying to prove this for all $\displaystyle n \geq 1 $

$\displaystyle (p-1)!^{p^{n-1}}\equiv -1\bmod p^n$

I think it's just a variation of Wilson's theorem but I can't seem to prove. I've tried induction but I can't change from $\displaystyle \bmod p^n$ to $\displaystyle \bmod p^{n+1}$

Any help would be great?