<p>You are given an integer array, <code>nums</code>, and an integer <code>k</code>. <code>nums</code> comprises of only <code>0</code>&#39;s and <code>1</code>&#39;s. In one move, you can choose two <strong>adjacent</strong> indices and swap their values.</p>

<p>Return <em>the <strong>minimum</strong> number of moves required so that </em><code>nums</code><em> has </em><code>k</code><em> <strong>consecutive</strong> </em><code>1</code><em>&#39;s</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,0,0,1,0,1], k = 2
<strong>Output:</strong> 1
<strong>Explanation:</strong> In 1 move, nums could be [1,0,0,0,<u>1</u>,<u>1</u>] and have 2 consecutive 1&#39;s.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,0,0,0,0,0,1,1], k = 3
<strong>Output:</strong> 5
<strong>Explanation:</strong> In 5 moves, the leftmost 1 can be shifted right until nums = [0,0,0,0,0,<u>1</u>,<u>1</u>,<u>1</u>].
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> nums = [1,1,0,1], k = 2
<strong>Output:</strong> 0
<strong>Explanation:</strong> nums already has 2 consecutive 1&#39;s.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= nums.length &lt;= 10<sup>5</sup></code></li>
	<li><code>nums[i]</code> is <code>0</code> or <code>1</code>.</li>
	<li><code>1 &lt;= k &lt;= sum(nums)</code></li>
</ul>

class Solution:
    def minMoves(self, nums: List[int], k: int) -> int:
        # Extract the indices of all '1's in the nums array
        positions = [i - index for index, i in enumerate(i for i, num in enumerate(nums) if num == 1)]
        
        # Calculate prefix sums of positions, used to calculate costs in O(1) time
        prefix_sum = [0] * (len(positions) + 1)
        for i in range(len(positions)):
            prefix_sum[i + 1] = prefix_sum[i] + positions[i]
        
        # Initialize minimum moves to a large value
        min_moves = float('inf')
        
        # Iterate over each possible segment of k consecutive 1's
        for i in range(len(positions) - k + 1):
            # Middle index of the current segment
            mid = i + k // 2
            
            # Calculate the cost for this segment using prefix sums
            left_cost = positions[mid] * (mid - i) - (prefix_sum[mid] - prefix_sum[i])
            right_cost = (prefix_sum[i + k] - prefix_sum[mid + 1]) - positions[mid] * (i + k - mid - 1)
            
            # Update the minimum moves
            min_moves = min(min_moves, left_cost + right_cost)
        
        return min_moves
24600