Difficulty: Hard
Tags: LeetCode, Hard, Stack, Binary Indexed Tree, Segment Tree, Array, Binary Search, Monotonic Stack, Heap (Priority Queue), leetcode-2940, O(n + qlogn), O(n), Heap, Mono Stack, Online Solution

Problem

You are given a 0-indexed array heights of positive integers, where heights[i] represents the height of the i^th building.

If a person is in building i, they can move to any other building j if and only if i < j and heights[i] < heights[j].

You are also given another array queries where queries[i] = [a_i, b_i]. On the i^th query, Alice is in building a_i while Bob is in building b_i.

Return an array ans where ans[i] is the index of the leftmost building where Alice and Bob can meet on the i^th query. If Alice and Bob cannot move to a common building on query i, set ans[i] to -1.

Example 1:

Input: heights = [6,4,8,5,2,7], queries = [[0,1],[0,3],[2,4],[3,4],[2,2]]
Output: [2,5,-1,5,2]
Explanation: In the first query, Alice and Bob can move to building 2 since heights[0] < heights[2] and heights[1] < heights[2]. 
In the second query, Alice and Bob can move to building 5 since heights[0] < heights[5] and heights[3] < heights[5]. 
In the third query, Alice cannot meet Bob since Alice cannot move to any other building.
In the fourth query, Alice and Bob can move to building 5 since heights[3] < heights[5] and heights[4] < heights[5].
In the fifth query, Alice and Bob are already in the same building.  
For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet.
For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet.

Example 2:

Input: heights = [5,3,8,2,6,1,4,6], queries = [[0,7],[3,5],[5,2],[3,0],[1,6]]
Output: [7,6,-1,4,6]
Explanation: In the first query, Alice can directly move to Bob's building since heights[0] < heights[7].
In the second query, Alice and Bob can move to building 6 since heights[3] < heights[6] and heights[5] < heights[6].
In the third query, Alice cannot meet Bob since Bob cannot move to any other building.
In the fourth query, Alice and Bob can move to building 4 since heights[3] < heights[4] and heights[0] < heights[4].
In the fifth query, Alice can directly move to Bob's building since heights[1] < heights[6].
For ans[i] != -1, It can be shown that ans[i] is the leftmost building where Alice and Bob can meet.
For ans[i] == -1, It can be shown that there is no building where Alice and Bob can meet.

Constraints:

1 <= heights.length <= 5 * 10⁴
1 <= heights[i] <= 10⁹
1 <= queries.length <= 5 * 10⁴
queries[i] = [a_i, b_i]
0 <= a_i, b_i <= heights.length - 1