<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 SGTree{
public:
  vector<int> sg;
    SGTree(int n){
        sg.resize(4*n+1);
    }
    void build(int sgidx,int l,int r,vector<int> &v){
        if(l>r){return ;}
        if(l==r){sg[sgidx]=v[l];return;}
           
         int mid=l+(r-l)/2;
         
         build(2*sgidx+1,l,mid,v);         
         build(2*sgidx+2,mid+1,r,v);
         
         sg[sgidx]=sg[2*sgidx+1]&sg[2*sgidx+2];
    }
    int query(int sgidx,int l,int r,int qs,int qe){
        if(r<qs||l>qe){return INT_MAX;}
        
        if(qs<=l and r<=qe){return sg[sgidx];}
        int mid=l+(r-l)/2;
        
        int left = query(2*sgidx+1,l,mid,qs,qe);
        int right = query(2*sgidx+2,mid+1,r,qs,qe);
        
        return left&right;
    }
    void update(int sgidx,int l,int r,int val,int idx){
        if(l>r){return;}
        if(l==r){sg[sgidx]=val;return;}
        
        int mid=l+(r-l)/2;
        
        if(idx>mid){
            l=mid+1;update(sgidx,mid+1,r,val,idx);
        }else{
            r=mid-1;update(sgidx,l,mid,val,idx);
        }
        
        sg[sgidx]=sg[2*sgidx+1]&sg[2*sgidx+2];
    }
};
class Solution {
public:
    int closestToTarget(vector<int>& v, int t) {
        int n=v.size();
        int mn=1e9;
        
        SGTree seg(n);
        seg.build(0,0,n-1,v);
    
        for(int i=0;i<n;i++)
        {
           int l=i,r=n-1;
           while(l<=r)
           {
               int mid=l+(r-l)/2;
               int a=seg.query(0,0,n-1,i,mid);
               if(a>t){l=mid+1;}
               else{
                   r=mid-1;
               }
               mn=min(mn,abs(a-t));
           }
        }

        return mn;
    }
};
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