<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>

class Solution {
public:
    static const int N = 1e5 + 7;
    int tree[4 * N];

    void build(int node, int s, int e, vector<int>& arr) {
        if (s == e) {
            tree[node] = arr[s];
            return;
        }
        int mid = (s + e) / 2;
        build(2 * node, s, mid, arr);
        build(2 * node + 1, mid + 1, e, arr);
        tree[node] = tree[2 * node] & tree[2 * node + 1];
    }

    int query(int node, int s, int e, int l, int r) {
        if (s > r || e < l) return INT_MAX;
        if (l <= s && e <= r) return tree[node];
        int mid = (s + e) / 2;
        int left = query(2 * node, s, mid, l, r);
        int right = query(2 * node + 1, mid + 1, e, l, r);
        return left & right; 
    }

    int closestToTarget(vector<int>& arr, int k) {
        int ans = INT_MAX;
        int n = arr.size();
        build(1, 0, n - 1, arr);
        for (int i = 0; i < n; i++) {
            int low = i, high = n - 1;
            while (low <= high) {
                int mid = (low + high) / 2;
                int current = query(1, 0, n - 1, i, mid);
                ans = min(ans, abs(k - current));
                if (current > k) {
                    low = mid + 1;
                } else if (current < k) {
                    high = mid - 1;
                } else {
                    return ans;
                }
            }
        }
        return ans;
    }
};

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