<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>

typedef long long int ll;
class Solution {
public:
    int minMoves(vector<int>& nums, int k) {
        vector<int>indices={0};
        for(int i=0;i<nums.size();i++){
            if(nums[i]==1)indices.push_back(i);
        }
        int n = indices.size();
        vector<ll>prefixSum(n,0);
        for (int i = 1; i <n ; ++i) {
            prefixSum[i] = prefixSum[i-1]+indices[i];
        }
        auto getRangeSum = [&](int l,int r)->int{
            return prefixSum[r]-(l>0?prefixSum[l-1]:0);
        };
        long long int minMove = LLONG_MAX;
        for (int l = 1,r=k; r <n ; ++l,r++) {
            int medianIdx = l+(r-l)/2;
            ll leftSum = getRangeSum(l,medianIdx);
            ll rightSum = getRangeSum(medianIdx,r);
            ll radius = medianIdx-l;
            long long reqMove = LLONG_MAX;
            if(k%2==0){
                reqMove = rightSum-leftSum - radius*1LL*(radius+1) - indices[medianIdx] - (radius+1) ;
            }else{
                reqMove = rightSum-leftSum - radius*1LL*(radius+1) ;
            }
            minMove = min(minMove,reqMove);
        }
        return (int)minMove;
    }
};

static const auto speedup = []() {
    std::ios::sync_with_stdio(false); std::cin.tie(nullptr); return 0;
}();
139000