Warm-up question: Given two binary strings $s\in \{0,1\}^n$ and $t\in \{0,1\}^{n+k}$, we say $s$ is the result of a k-deletion on $t$ if $s$ is a (not necessarily contiguous) substring of $t$, which we denote by $s\subseteq t$. Given $s\in \{0,1\}^n$ and $k\in \mathbb{N}$, consider
\begin{equation*}
A_{s,k} =\{ t\in \{0,1\}^{n+k} \colon s\subseteq t \}.
\end{equation*}
Determine the size of $A_{s,k}$ in terms of $s$ and $k$.