Beautiful Flip

Define the *beauty* of a **binary** string to be the minimum of the number of zeros and the number of ones present in it. For example, the beauty of $\texttt{111}$ is $0$, while the beauty of $\texttt{1001100}$ is $3$. You are given a binary string $S$ of length $N$, along with an integer $K$. At most once, you can do the following: - Choose a substring of $S$ of length **at most** $K$, and