\begin{tutorial}{Anton buys a piglet}

\begin{center}
\begin{tabular}{rl}
\textbf{Problem Author}: & \textbf{Feysa Bohdan} \\
\textbf{Prepared by}: & \textbf{Feysa Bohdan} \\
\textbf{Tutorial by}: & \textbf{Pavlo Tsitsei} 
\end{tabular} 
\end{center}

To determine if a sequence of operations exists: if $x$ is not divisible by $2^k$, then the answer is $-1$, as there is no such sequence. Otherwise, it is always possible to create such a number. At a minimum, this can be done in $\frac{x}{2^k}$ operations each time using the second button.

To find the sequence of these operations, a greedy algorithm can be used. Let's say we have already used the first button $q$ times and $x$ has $n$ bits. Then, to determine whether we need to add $2^k$ first or continue using the first button, we need to check the $n-q$-th bit of the number $x$. If it is equal to 1, then before the operation, $2^k$ needs to be added. These actions need to be repeated until we get the number $x$.

\end{tutorial}
