<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>


#define lson rt << 1
#define rson rt << 1 | 1
#define mid ((l + r) >> 1)
#define Lson l, mid, lson
#define Rson mid + 1, r, rson

const int maxn = 1e5 + 10;
int sum[maxn << 2];
void pushup(int rt) {
    sum[rt] = sum[rson] & sum[lson];
}
void build(int l, int r, int rt, vector<int>& arr) {
    if (l == r) {
        sum[rt] = arr[l-1];
        return;
    }
    build(Lson, arr), build(Rson, arr);
    pushup(rt);
}
int query(int L, int R, int l, int r, int rt) {
    if (L <= l && R >= r) {
        return sum[rt];
    }
    int ret = (1 << 30) - 1;
    if (L <= mid) ret &= query(L, R, Lson);
    if (R > mid) ret &= query(L, R, Rson);
    return ret;
}

class Solution {
public:
    int closestToTarget(vector<int>& arr, int target) {
        int n = arr.size();
        int ret = 0x3f3f3f3f;
        for (auto it : arr) {
            ret = min(ret, abs(it - target));
        }
        build(1, n, 1, arr);

        for (int tagl = 1; tagl <= n; tagl++) {
            int l = tagl, r = n, ans = 0x3f3f3f3f, idx = -1;
            while (l <= r) {
                int m = (l + r) / 2;
                int qres = query(tagl, m, 1, n, 1);
                int t = qres - target;
                if (t > 0) {
                    ans = qres;
                    idx = m;
                    l = mid + 1;
                }
                else if (t == 0) {
                    return 0;
                }
                else if (t < 0) {
                    r = mid - 1;
                }
            }
            if (ans != 0x3f3f3f3f) {
                ret = min(ret, abs(ans - target));
                if (idx != n) {
                    ans &= arr[idx];
                    ret = min(ret, abs(ans - target));
                }
            }
        }
        return ret;
    }
};
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