Remove an interval by index and simplify (merge) cover intervals

You are given a string book and a list of intervals cover, where each interval (start, end) (possibly out of order) represents a substring cut from book. The collection of these substrings forms a cipher. Task 1: Remove an interval by index Remove the interval at position idx in the cover list (note: idx refers to the index in cover, not an index in book) and return the updated cover. Task 2: Produce a simplified cipher after removal After removing cover[idx], simplify the remaining intervals so that no two intervals are mergeable. Equivalently, merge all intervals that overlap or are adjacent. Return: the merged interval list sorted by start, and the final cipher string obtained by concatenating book[start..end] (inclusive) for each merged interval in order. Constraints 0 <= start <= end < n cover may be unsorted intervals may overlap or be adjacent 0 <= idx < len(cover) Example book = "abcdefghijk", cover = [(2,4),(0,1),(5,6)], idx=1. After removal: [(2,4),(5,6)]. After merging adjacency: [(2,6)]. Cipher: "cdefg". Example Input book=abcdefghijk cover=[(2,4),(0,1),(5,6)] idx=1 Output merged=[(2,6)] cipher=cdefg