Stock-based Compensation - Schedule of Restricted Stock Units Activity (Details) - Restricted Stock Units - USD ($) $ / shares in Units, $ in Thousands	12 Months Ended
	Aug. 31, 2024	Aug. 31, 2023	Aug. 31, 2022
Number of Units
Beginning outstanding (in shares)	79,816
Granted (in shares)	19,201
Converted to shares of common stock (in shares)	(28,658)
Forfeited (in shares)	(211)
Ending outstanding (in shares)	70,148	79,816
Vested (in shares)	45,113
Weighted-Average Grant Date Fair Value Per Unit
Beginning outstanding (in dollars per share)	$ 144.24
Granted (in dollars per share)	206.85	$ 167.05	$ 217.03
Converted to shares of common stock (in dollars per share)	137.42
Forfeited (in dollars per share)	188.85
Ending outstanding (in dollar par share)	164.03	$ 144.24
Vested (in dollars per share)	$ 149.81
Outstanding, aggregate intrinsic value	$ 18,438
Vested, Aggregate Intrinsic Value	$ 11,858