Counting MEX Is Fun

For a sequence $B$, the MEX (minimum excluded value) of $B$, denoted as $MEX(B)$, is the smallest non-negative integer that does not appear in $B$. You are given two integers $N$ and $K$. Consider all permutations $P$ of the integers {$0, 1, ..., N-1$}. For a permutation $P$, define a set $S(P)$ containing all distinct MEX values of all its subarrays. Formally, $S(P)$ = { $MEX(P[l..r]) |