Remove one point from a cover of integer intervals

You are given a list of non-overlapping half-open intervals. An interval [start, end] with start < end covers the integers start, start + 1, ..., end - 1. Reading the intervals in the order they are given, and each interval from left to right, produces a flattened sequence of covered integers. The list is not necessarily sorted.

Implement remove_covered_point(intervals, idx), which removes the integer at 0-based position idx of the flattened sequence and returns the resulting list of intervals.

• Keep the input order. Do not sort or merge intervals.
• Removing a point from the middle of an interval splits it into two intervals.
• Never return an empty interval (start == end).
• Raise an error if idx is negative or not less than the number of covered integers.
• Intervals can be very long (lengths up to 10^9), so do not expand them into points.

Example 1

intervals = [[10, 13], [2, 4]]   # flattened: 10, 11, 12, 2, 3
idx = 1                          # removes 11
-> [[10, 11], [12, 13], [2, 4]]

Example 2

intervals = [[5, 6], [0, 2]]     # flattened: 5, 0, 1
idx = 0                          # removes 5; its interval disappears
-> [[0, 2]]

Part 2. The same cover now receives many removals in a row. Support remove(idx) (returns the removed integer) and to_intervals() efficiently.