Implement minimum window substring with counts

Implement a function min_window_with_counts(s: str, t: str) -> tuple[int,int] that returns the (start_index, end_index) of the shortest substring of s containing all characters in t with at least their required multiplicities. Constraints and rules: - ASCII strings; case-sensitive; indices are 0-based; return (-1, -1) if no window exists. - The window cannot skip characters; whitespace and punctuation in s count as normal characters. - If multiple windows have the same minimal length, return the one with the smallest start index; if still tied, the one with the smallest end index. - Time complexity must be O(n) and space O(Σ) using a sliding window and frequency maps; do not sort or use nested scans over s. - You must handle large inputs (len(s) up to 2e6) without quadratic behavior. Provide at least 3 test cases, including: 1) s = "ADOBECODEBANC", t = "ABC" -> expected (9, 12) for "BANC". 2) s = "aAaBbBc", t = "Aab" -> expected (0, 3) for "aAaB" (meets counts: A×2, a×1, b×1) or any equally minimal valid window following tie-breaking. 3) s = "xyzzzy", t = "zz" -> expected (2, 3). Explain how your code maintains counts and a satisfied counter.