Minimum Moves to Pick K Ones

Choose any start index and, using at most maxChanges zero→one flips (each counting as a move) and adjacent swaps of 1s toward your position (each swap counts as a move; picking a 1 at your index is free), collect exactly k ones with minimum moves. Algorithmically this is about selecting k target positions (possibly turning some zeros into ones) and minimizing the total adjacent-swap distance to aggregate them at some center under a flip budget, typically handled by working on the positions-of-ones with sliding-window/prefix-cost techniques.