Binary Removals

Given a **binary** string $S$ of length $N$, and two integers $X$ and $K$. Your task is to empty the string by performing the following operation : - In one operation, you may select any subsequence$^{\dagger}$ of the string such that the number of **inversions**$^{\dagger}$ in the subsequence lies in the range $[0, X]$ and is divisible by $K$. - Remove the selected subsequence from the string.