Problem Overview

You are given an array of non-overlapping intervals sorted by start position. Each interval represents a range of consecutive integers. You are also given an index into the "flattened" or "covered" list of all elements across all intervals. Your task is to remove the element at that index from the covered list and return the resulting interval array.

This problem tests understanding of:

• Interval manipulation and merging

• Efficient indexing without building full arrays

• Edge case handling (start, end, middle, single-element intervals)

• Space-time trade-offs

Key Points

• Intervals are non-overlapping and sorted

• The index refers to the position in the flattened list of all covered elements

• After removing an element, you may need to split an interval into two parts

• Both endpoints are inclusive: (4, 7) represents [4, 5, 6, 7]

Example

` intervals = [(4, 7), (10, 11), (13, 15)] index = 2

Covered list: [4, 5, 6, 7, 10, 11, 13, 14, 15]

Index 2 points to element 6

After removing 6: [4, 5, 7, 10, 11, 13, 14, 15]

Result: [(4, 5), (7, 7), (10, 11), (13, 15)]

`

Requirements

• 1 <= len(intervals) <= 10^4

• 0 <= intervals[i][0] <= intervals[i][1] <= 10^9