<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 {
public:
    int minMoves(std::vector<int>& nums, int k) {
        std::vector<long long> indices;
        indices.push_back(0); 

        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == 1) {
                indices.push_back(i);
            }
        }

        int n = indices.size();
        std::vector<long long> prefixSums(n, 0);
        for (int i = 1; i < n; ++i) {
            prefixSums[i] = indices[i] + prefixSums[i - 1];
        }

        long long minMoves = INT_MAX;

        for (int left = 1, right = k; right < n; ++left, ++right) {
            int mid = (left + right) / 2;
            int radius = mid - left;
            long long rightSum = prefixSums[right] - prefixSums[mid];
            long long leftSum = prefixSums[mid - 1] - prefixSums[left - 1];
            long long adjustment = (radius) *1LL* (radius + 1);

            if (k % 2 == 0) {
                leftSum += indices[mid];
                adjustment += (radius + 1);
            }

            minMoves = std::min(minMoves, rightSum - leftSum - adjustment);
        }

        return minMoves;
    }
};


static const auto speedup = []() {
    std::ios::sync_with_stdio(false); std::cin.tie(nullptr); return 0;
}();

147400