<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(vector<int>& nums, int k) {
        /*
        Idea: for a window of K ones, find min swaps to group all ones at one index
        return min - number of swaps required to distribute 1's
        */
        const int extra = (k % 2) == 1 ? 0 : 1;
        const int64_t radius = (k - 1 - extra) / 2;

        vector<int> oneIdx; oneIdx.reserve(nums.size());
        for (int i = 0; i < nums.size(); ++i) {
            if (nums[i] == 1) oneIdx.push_back(i);
        }
        const int n = oneIdx.size();
        if (n < k)
            return -1;

        vector<int64_t> prefSum(n + 1, 0);
        for (int i = 1; i <= n; ++i) {
            prefSum[i] = prefSum[i-1] + oneIdx[i-1];
        }

        int64_t result = numeric_limits<int64_t>::max();
        for (int i = radius; i < n - radius - extra; ++i) {
            const int64_t right = prefSum[i + radius + 1 + extra] - prefSum[i+1];
            const int64_t left = prefSum[i] - prefSum[i-radius];
            result = min(result, right - left - extra * oneIdx[i]);
        }
        return result - (radius + extra) * (radius + 1);
    }
};
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