Suppose a function $f$ is 22 times differentiable and $f^{(22)}=f$. Then, it turns out that $f$ is infinitely differentiable and that for any positive number $n$, $f^{(n)}$ equals one of the functions $f, \; f', \; f'', \; ... \; , \; f^{(21)}$.
So, find a positive number $k$ so that $f^{(114)}=f^{(k)}$ and $0 \leq k \leq 21$.

$k =$