Basics: which cells a Fenwick tree touches

A Fenwick tree is a 1-indexed array t[1..n] where cell j stores the sum of the original values at positions j - lowbit(j) + 1 .. j, and lowbit(j) = j & -j is the value of the lowest set bit of j. Both operations are just walks over indexes. Write those walks, returning the indexes instead of doing any sums:

• lowbit(i) -> int: the lowest set bit of i (for i >= 1).
• update_indexes(i, n) -> list[int]: the cells, in visiting order, that add(i, delta) changes: start at i, then repeatedly add lowbit, while the index is <= n. These are exactly the cells whose range contains position i.
• query_indexes(i) -> list[int]: the cells, in visiting order, that prefix_sum(i) reads: start at i, then repeatedly subtract lowbit, while the index is > 0. Their ranges fit together to cover 1..i exactly once. query_indexes(0) is [].

lowbit(12)               # 4       (12 = 0b1100)
update_indexes(5, 16)    # [5, 6, 8, 16]
query_indexes(13)        # [13, 12, 8]   ranges 13..13, 9..12, 1..8

Constraints: 1 <= i <= n for update_indexes, 0 <= i for query_indexes.