<p><img alt="" src="https://assets.leetcode.com/uploads/2020/07/09/change.png" style="width: 635px; height: 312px;" /></p>

<p>Winston was given the above mysterious function <code>func</code>. He has an integer array <code>arr</code> and an integer <code>target</code> and he wants to find the values <code>l</code> and <code>r</code> that make the value <code>|func(arr, l, r) - target|</code> minimum possible.</p>

<p>Return <em>the minimum possible value</em> of <code>|func(arr, l, r) - target|</code>.</p>

<p>Notice that <code>func</code> should be called with the values <code>l</code> and <code>r</code> where <code>0 &lt;= l, r &lt; arr.length</code>.</p>

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

<pre>
<strong>Input:</strong> arr = [9,12,3,7,15], target = 5
<strong>Output:</strong> 2
<strong>Explanation:</strong> Calling func with all the pairs of [l,r] = [[0,0],[1,1],[2,2],[3,3],[4,4],[0,1],[1,2],[2,3],[3,4],[0,2],[1,3],[2,4],[0,3],[1,4],[0,4]], Winston got the following results [9,12,3,7,15,8,0,3,7,0,0,3,0,0,0]. The value closest to 5 is 7 and 3, thus the minimum difference is 2.
</pre>

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

<pre>
<strong>Input:</strong> arr = [1000000,1000000,1000000], target = 1
<strong>Output:</strong> 999999
<strong>Explanation:</strong> Winston called the func with all possible values of [l,r] and he always got 1000000, thus the min difference is 999999.
</pre>

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

<pre>
<strong>Input:</strong> arr = [1,2,4,8,16], target = 0
<strong>Output:</strong> 0
</pre>

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

<ul>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>5</sup></code></li>
	<li><code>1 &lt;= arr[i] &lt;= 10<sup>6</sup></code></li>
	<li><code>0 &lt;= target &lt;= 10<sup>7</sup></code></li>
</ul>

struct Region {
    int start, end;

    Region(int start, int end)
        : start(start), end(end) {}
};

class Solution {
public:
    int closestToTarget(vector<int>& arr, int target) {
        int n = arr.size();
        vector<deque<Region>> regions(20);  // arr[i] <= 10^6 < 2^20

        for (int i = n - 1; 0 <= i; --i) {
            for (int j = 0, mask = 1; j < 20; ++j, mask <<= 1) {
                if ((arr[i] & mask) == 0) {
                    continue;
                }

                if (regions[j].empty() || i != regions[j].front().start - 1) {
                    regions[j].push_front(Region(i, i));
                } else {
                    regions[j].front().start -= 1;
                }
            }
        }

        int prefix = arr[0], res = abs(prefix - target);
        for (int head = 0, tail = 1; tail < n && 0 < res; ++tail) {
            prefix &= arr[tail];

            while (head < tail && prefix < target) {
                res = min(res, target - prefix);
                ++head;

                for (int k = 0, mask = 1; k < 20; ++k, mask <<= 1) {
                    if (!regions[k].empty()) {
                        Region region = regions[k].front();

                        if (region.end == head - 1) {
                            regions[k].pop_front();
                        } else if (region.start <= head && tail <= region.end) {
                            prefix |= mask;
                        }
                    }
                }
            }

            res = min(res, abs(prefix - target));
        }

        return res;
    }
};
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