Yet Another Flipping Problem

Chef has a binary string $S$ of length $N$, where the first $K$ characters of $S$ are '$\texttt{1}$', while the rest are '$\texttt{0}$'. He wants to make all the characters equal to '$\texttt{0}$'. You are allowed to perform the following operation on the string $S$ as long as $2^{i-1} \leq N$: - In the $i^{th}$ operation, you can select any contiguous range of $2^{i-1}$ indices of $S$ and flip th