<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>

template <typename t> class SEGtree{
    private:

    vector<t> seg;
    public:
    SEGtree(int n){
       seg.resize(4*n+1);
    }
    void build(int low,int high,vector<t>& arr,int ind){
        if(low==high){
            seg[ind]=arr[low];
            return;
        }
        t mid=low+(high-low)/2;
        build(low,mid,arr,2*ind+1);
        build(mid+1,high,arr,2*ind+2);
        seg[ind]=seg[2*ind+1] & seg[2*ind+2];
        return;
    }
    //l,r->represents the range of query whose result is to be known
    t query(int low,int high,int l,int r,int ind){
        if(high<l || low>r) return INT_MAX; //no overlap
        if(low>=l && high<=r) return seg[ind]; //complete overlap
        int mid=low+(high-low)/2;
        int left=query(low,mid,l,r,2*ind+1);
        int right=query(mid+1,high,l,r,2*ind+2);
        return left & right;
    }
};
class Solution {
public:
    int closestToTarget(vector<int>& arr, int tar) {
        int n=arr.size();
        SEGtree<int>* obj=new SEGtree<int>(n);
        obj->build(0,n-1,arr,0);
        int ans=INT_MAX;
        for(int i=0;i<n;i++){
            int st=i;
            int end=n-1;
            int mid=(st+end)>>1;
            while(st<=end){
                mid=(st+end)>>1;
                int x=obj->query(0,n-1,i,mid,0);
                if(tar>x){
                    ans=min(ans,tar-x);
                    end=mid-1;
                }
                else {
                    ans=min(ans,x-tar);
                    st=mid+1;
                }
            }
        }
        return ans;
    }
};
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