Count Good Strings

Problem Overview

• Given N, count length-2N strings over A and B that are "good": exactly N A's, N B's, and in every prefix count(A) ≥ count(B).
• Input: integer N; Output: number of good strings modulo 10000.
• Domain: string combinatorics and prefix-balance validation, akin to balanced sequences.
• This coding interview problem is a Commvault interview question from their interviews.
• Large counts are expected; require modulo handling.