Flip to Invert

JJ has a binary string $S$ of length $N$. JJ can perform the following operation on $S$: - Select an $i$ such that $1 \le i \le N$, and flip $S_i$ (i.e. change $0$ to $1$ and $1$ to $0$) JJ wants to minimize the number of inversions in $S$ by performing the above operation **at most** $K$ times. Can you help JJ do so? Recall that a pair of indices $(i, j)$ in $S$ is called an inversion if $i \lt