<p>Given a <strong>sorted</strong> integer array <code>arr</code>, two integers <code>k</code> and <code>x</code>, return the <code>k</code> closest integers to <code>x</code> in the array. The result should also be sorted in ascending order.</p>

<p>An integer <code>a</code> is closer to <code>x</code> than an integer <code>b</code> if:</p>

<ul>
	<li><code>|a - x| &lt; |b - x|</code>, or</li>
	<li><code>|a - x| == |b - x|</code> and <code>a &lt; b</code></li>
</ul>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<pre><strong>Input:</strong> arr = [1,2,3,4,5], k = 4, x = 3
<strong>Output:</strong> [1,2,3,4]
</pre><p><strong class="example">Example 2:</strong></p>
<pre><strong>Input:</strong> arr = [1,2,3,4,5], k = 4, x = -1
<strong>Output:</strong> [1,2,3,4]
</pre>
<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>1 &lt;= k &lt;= arr.length</code></li>
	<li><code>1 &lt;= arr.length &lt;= 10<sup>4</sup></code></li>
	<li><code>arr</code> is sorted in <strong>ascending</strong> order.</li>
	<li><code>-10<sup>4</sup> &lt;= arr[i], x &lt;= 10<sup>4</sup></code></li>
</ul>

class Solution {
public:
    vector<int> findClosestElements(vector<int>& arr, int k, int x) {
        vector<int> ans;
        // find index of x
        int n = arr.size();
        int left = 0, right = n -1;
        int x_id;
        while(left < right){
            int mid = left + (right - left)/2;
            if(arr[mid] < x) { 
                left = mid +1;
            }
            else {
                right = mid;
            }
        }
        int low = left -1 , high =left;
        while(k --){
            if(low < 0){
                ans.push_back(arr[high++]);}
            else if(high >= n){
                ans.push_back(arr[low--]);}
            else if(abs(arr[low]-x)<=abs(arr[high]-x)){
                ans.push_back(arr[low--]);}
            else{ans.push_back(arr[high++]);}
        }
        sort(ans.begin(),ans.end());
        return ans;
    }
};
// |a-x| < |b -x| <=> a -x < b - x or a - x > x - b <=> a < b or a + b > 2x
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