Romantic Reversals

Alice initially has a string $S$ of length $N$, and she decides to modify it! Her modification consists of $K$ steps numbered from $1$ to $K$. In the $i$-th step, Alice reverses the prefix of length $i$ of $S$. For example, suppose Alice starts with $S = \texttt{abferty}$, and she modifies it via $3$ steps, then: - After the first step, $\textcolor{blue}{\texttt{a}}\texttt{bferty} \rightarrow S =