You are given a $0$-indexed binary array nums of length n, a positive integer k, and a non-negative integer maxChanges.

Alice plays a game where her objective is to collect k ones. At the beginning of the game, Alice selects an index aliceIndex such that $0 \leq$ aliceIndex $< n$. If nums[aliceIndex] is equal to $1$, Alice immediately collects it, and nums[aliceIndex] becomes $0$.

Afterward, in each move, Alice can perform one of the following actions:

1. Select an index j such that $0 \leq j < n$ and nums[j] = 0, then set nums[j] = 1. This action can be performed at most maxChanges times in total throughout the game.

2. Select two adjacent indices x and y such that $|x - y| = 1$, nums[x] = 1, and nums[y] = 0, then swap the values of nums[x] and nums[y]. If y is equal to aliceIndex, Alice immediately collects the one, and nums[y] becomes $0$.

Return the minimum number of moves required for Alice to collect k ones.

Constraints:

• $2 \leq$ n $\leq 10^5$

• $0 \leq$ nums[i] $\leq 1$

• $1 \leq$ k $\leq 10^5$

• $0 \leq$ maxChanges $\leq 10^5$

• maxChanges $+ ext{sum}($nums$) \geq$ k

Now, let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Implement your solution in the following coding playground.