MEX Sequences

Chef is learning about **absolute** [MEX](https://en.wikipedia.org/wiki/Mex_(mathematics)) sequences. A sequence $A$ of $N$ integers is said to be an **absolute** MEX sequence, if the following property holds for all $1\le i \le N$: - $|A_i - \texttt{MEX} (A_1, A_2, \dots, A_i)| \leq 1$ Chef has two integers $N$ and $M$. Find the total number of **absolute** MEX sequences $A$, of length $N$, su