<p>There is a hotel with <code>n</code> rooms. The rooms are represented by a 2D integer array <code>rooms</code> where <code>rooms[i] = [roomId<sub>i</sub>, size<sub>i</sub>]</code> denotes that there is a room with room number <code>roomId<sub>i</sub></code> and size equal to <code>size<sub>i</sub></code>. Each <code>roomId<sub>i</sub></code> is guaranteed to be <strong>unique</strong>.</p>

<p>You are also given <code>k</code> queries in a 2D array <code>queries</code> where <code>queries[j] = [preferred<sub>j</sub>, minSize<sub>j</sub>]</code>. The answer to the <code>j<sup>th</sup></code> query is the room number <code>id</code> of a room such that:</p>

<ul>
	<li>The room has a size of <strong>at least</strong> <code>minSize<sub>j</sub></code>, and</li>
	<li><code>abs(id - preferred<sub>j</sub>)</code> is <strong>minimized</strong>, where <code>abs(x)</code> is the absolute value of <code>x</code>.</li>
</ul>

<p>If there is a <strong>tie</strong> in the absolute difference, then use the room with the <strong>smallest</strong> such <code>id</code>. If there is <strong>no such room</strong>, the answer is <code>-1</code>.</p>

<p>Return <em>an array </em><code>answer</code><em> of length </em><code>k</code><em> where </em><code>answer[j]</code><em> contains the answer to the </em><code>j<sup>th</sup></code><em> query</em>.</p>

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

<pre>
<strong>Input:</strong> rooms = [[2,2],[1,2],[3,2]], queries = [[3,1],[3,3],[5,2]]
<strong>Output:</strong> [3,-1,3]
<strong>Explanation: </strong>The answers to the queries are as follows:
Query = [3,1]: Room number 3 is the closest as abs(3 - 3) = 0, and its size of 2 is at least 1. The answer is 3.
Query = [3,3]: There are no rooms with a size of at least 3, so the answer is -1.
Query = [5,2]: Room number 3 is the closest as abs(3 - 5) = 2, and its size of 2 is at least 2. The answer is 3.</pre>

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

<pre>
<strong>Input:</strong> rooms = [[1,4],[2,3],[3,5],[4,1],[5,2]], queries = [[2,3],[2,4],[2,5]]
<strong>Output:</strong> [2,1,3]
<strong>Explanation: </strong>The answers to the queries are as follows:
Query = [2,3]: Room number 2 is the closest as abs(2 - 2) = 0, and its size of 3 is at least 3. The answer is 2.
Query = [2,4]: Room numbers 1 and 3 both have sizes of at least 4. The answer is 1 since it is smaller.
Query = [2,5]: Room number 3 is the only room with a size of at least 5. The answer is 3.</pre>

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

<ul>
	<li><code>n == rooms.length</code></li>
	<li><code>1 &lt;= n &lt;= 10<sup>5</sup></code></li>
	<li><code>k == queries.length</code></li>
	<li><code>1 &lt;= k &lt;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= roomId<sub>i</sub>, preferred<sub>j</sub> &lt;= 10<sup>7</sup></code></li>
	<li><code>1 &lt;= size<sub>i</sub>, minSize<sub>j</sub> &lt;= 10<sup>7</sup></code></li>
</ul>

class Solution:
    def closestRoom(self, R: List[List[int]], Q: List[List[int]]) -> List[int]:
        R.sort(key = lambda x: (x[1], x[0]))
        Q = [(qid,size,i) for i, (qid, size) in enumerate(Q)]
        Q.sort(key = lambda x: (x[1], x[0], x[2]), reverse = True)
        ans = [-1] * len(Q)
        X = []
        for qid, size, i in Q:
            while R and R[-1][1] >= size:
                idr, _ = R.pop()
                bisect.insort(X, idr)
            if X:
                j = bisect.bisect(X, qid)
                if j == len(X): ans[i] = X[-1]
                elif j == 0: ans[i] = X[0]
                else:
                    if X[j] - qid < qid - X[j-1]: ans[i] = X[j]
                    else: ans[i] = X[j-1]
        return ans
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