Anton decided not to save money, but to buy a piglet. To help with the money, he turned to his acquaintance, the wizard Kozak Vusa. It so happened that Kozak Vusa was too busy preparing special smoothies of the "B" brand, so he simply decided to give Anton two magic buttons:
\begin{enumerate}
\item pressing the first button doubles his balance;
\item pressing the second button adds exactly $2^k$ coins to his balance.
\end{enumerate}
At the underground piglet auction, Anton saw that the cheapest beautiful piglet costs $x$ karbovanets.

He was about to start pressing the buttons, but remembered that for such manipulations, the employees of "Polybank" could sue him. Therefore, he decided that he would try to get \textbf{exactly} $x$ coins, after which he would immediately buy the piglet and again have exactly $0$ karbovanets in his account.

Now you need to help Anton with a plan of action, and if possible, determine the minimum number of operations needed and output the order of operations. For this, Anton promised to let you play "Calculator Online" on his laptop.