Stockholders' Equity - Accumulated Other Comprehensive Loss (Details) - USD ($) $ in Thousands	Feb. 28, 2023	Nov. 30, 2022	Aug. 31, 2022	Feb. 28, 2022	Nov. 30, 2021	Aug. 31, 2021
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ 1,607,154	$ 1,474,128	$ 1,331,408	$ 1,215,981	$ 1,098,895	$ 1,016,353
Accumulated Other Comprehensive Loss
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	(92,243)	$ (93,059)	(108,383)	$ (55,848)	$ (57,670)	$ (38,962)
Accumulated unrealized gains (losses) on cash flow hedges, net of tax
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	7,450		3,149
Accumulated foreign currency translation adjustments
Accumulated Other Comprehensive Income (Loss) [Line Items]
Total AOCL	$ (99,693)		$ (111,532)