<p>You are given an array of non-overlapping intervals <code>intervals</code> where <code>intervals[i] = [start<sub>i</sub>, end<sub>i</sub>]</code> represent the start and the end of the <code>i<sup>th</sup></code> interval and <code>intervals</code> is sorted in ascending order by <code>start<sub>i</sub></code>. You are also given an interval <code>newInterval = [start, end]</code> that represents the start and end of another interval.</p>

<p>Insert <code>newInterval</code> into <code>intervals</code> such that <code>intervals</code> is still sorted in ascending order by <code>start<sub>i</sub></code> and <code>intervals</code> still does not have any overlapping intervals (merge overlapping intervals if necessary).</p>

<p>Return <code>intervals</code><em> after the insertion</em>.</p>

<p><strong>Note</strong> that you don&#39;t need to modify <code>intervals</code> in-place. You can make a new array and return it.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>

<pre>
<strong>Input:</strong> intervals = [[1,3],[6,9]], newInterval = [2,5]
<strong>Output:</strong> [[1,5],[6,9]]
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> intervals = [[1,2],[3,5],[6,7],[8,10],[12,16]], newInterval = [4,8]
<strong>Output:</strong> [[1,2],[3,10],[12,16]]
<strong>Explanation:</strong> Because the new interval [4,8] overlaps with [3,5],[6,7],[8,10].
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>0 &lt;= intervals.length &lt;= 10<sup>4</sup></code></li>
	<li><code>intervals[i].length == 2</code></li>
	<li><code>0 &lt;= start<sub>i</sub> &lt;= end<sub>i</sub> &lt;= 10<sup>5</sup></code></li>
	<li><code>intervals</code> is sorted by <code>start<sub>i</sub></code> in <strong>ascending</strong> order.</li>
	<li><code>newInterval.length == 2</code></li>
	<li><code>0 &lt;= start &lt;= end &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    vector<vector<int>> insert(vector<vector<int>>& intervals, vector<int>& target) {
        const int n = intervals.size();
        if (n == 0) return {target};

        int x = 0, y = n-1;
        while (x <= y) {
            int mid = (x + y) >> 1;
            if (intervals[mid][0] >= target[0]) {
                y = mid - 1;
            } else {
                x = mid + 1;
            }
        }

        if (x > 0 && intervals[x-1][1] >= target[0]) {
            intervals[x-1][0] = min(intervals[x-1][0], target[0]);
            intervals[x-1][1] = max(intervals[x-1][1], target[1]);
            x--;
        } else if (x < n && intervals[x][0] <= target[1]) {
            intervals[x][0] = min(intervals[x][0], target[0]);
            intervals[x][1] = max(intervals[x][1], target[1]);
        } else {
            intervals.insert(intervals.begin() + x, target);
        }

        int prevEnd = x > 0 ? intervals[x-1][1] : -1;
        int nextStart = x < n -1 ? intervals[x+1][0] : 200000;

        if (target[1] < nextStart && target[0] > prevEnd) {
            return intervals;
        }

        vector<vector<int>> ans;
        ans.push_back(intervals[0]);
        for (auto& i : intervals) {
            int &start = ans.back()[0], &end = ans.back()[1];
            if (i[0] > end) {
                ans.push_back(i);
            } else {
                start = min(start ,i[0]);
                end = max(end ,i[1]);
            }
        }
        return ans;
    }
};

auto boom = [](){
    ios_base::sync_with_stdio(0);
    cin.tie(0);
    cout.tie(0);
    return 0;
}();
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