Stock-Based Compensation - Schedule of Nonvested Stock Activity (Details) - Nonvested Stock Awards [Member] - $ / shares	3 Months Ended	12 Months Ended
	Dec. 31, 2021	Dec. 31, 2022	Sep. 30, 2021	Sep. 30, 2020
Number of Shares
Nonvested, beginning of period (in shares)	394,888	308,941	346,808	411,510
Granted (in shares)	63,800	255,375	307,025	183,725
Forfeited (in shares)	(4,428)	(26,020)	(36,545)	(27,076)
Vested (in shares)	(145,319)	(174,635)	(222,400)	(221,351)
Nonvested, end of period (in shares)	308,941	363,661	394,888	346,808
Weighted-Average Per Share Fair Value
Nonvested, beginning of period (in dollars per share)	$ 81.58	$ 90.10	$ 79.44	$ 72.66
Granted (in dollars per share)	114.89	109.66	82.80	87.82
Forfeited (in dollars per share)	86.08	97.24	78.81	80.57
Vested (in dollars per share)	77.97	88.98	80.39	73.64
Nonvested, end of period (in dollars per share)	$ 90.10	$ 103.86	$ 81.58	$ 79.44