Split a string into blocks that match the prefix's letter counts

You get a string s of uppercase letters A-Z.

Call a positive length L valid when:

• L <= len(s) and s can be cut into consecutive, non-overlapping blocks of exactly L characters with nothing left over, and
• every block contains each letter the same number of times as the prefix s[:L] does.

The blocks do not have to be equal strings; only their letter counts must match the prefix.

Implement valid_prefix_lengths(s: str) -> list[int] that returns all valid lengths in increasing order. (len(s) is always valid.)

Constraints: 1 <= len(s) <= 10^5.

Example 1

s = "ABCCBAACB"
output: [3, 9]

With L = 3 the blocks are ABC, CBA, ACB, each with one A, one B and one C. L = 1 fails because B differs from A.

Example 2

s = "ABBAAABB"
output: [4, 8]

L = 2 fails: the prefix AB has one of each letter, but the block AA does not. L = 4 works: ABBA and AABB each have two As and two Bs.

Reconstructed from the reported question; details may differ from what interviewers ask.