Income Taxes - Provision for Income Taxes (Details) - USD ($) $ in Thousands	3 Months Ended
Nov. 30, 2022	Nov. 30, 2021
Income Tax Disclosure [Abstract]
Income before income taxes	$ 157,885	$ 119,930
Provision for income taxes	$ 21,087	$ 12,283
Effective tax rate	13.40%	10.20%

Amount of income (loss) from continuing operations, including income (loss) from equity method investments, before deduction of income tax expense (benefit), and income (loss) attributable to noncontrolling interest.

Reference 1: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 32
-Subparagraph (c)
-URI https://asc.fasb.org/extlink&oid=126901519&loc=d3e8933-108599

Reference 2: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 30
-Subparagraph (b)
-URI https://asc.fasb.org/extlink&oid=126901519&loc=d3e8906-108599

Reference 3: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 32
-Subparagraph (f)
-URI https://asc.fasb.org/extlink&oid=126901519&loc=d3e8933-108599

Reference 4: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 940
-SubTopic 20
-Section 25
-Paragraph 1
-URI https://asc.fasb.org/extlink&oid=126941158&loc=d3e41242-110953

Reference 5: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 22
-URI https://asc.fasb.org/extlink&oid=126901519&loc=d3e8736-108599

Reference 6: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 220
-SubTopic 10
-Section S99
-Paragraph 2
-Subparagraph (SX 210.5-03(10))
-URI https://asc.fasb.org/extlink&oid=126953954&loc=SL114868664-224227

Reference 7: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 944
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.7-04(8))
-URI https://asc.fasb.org/extlink&oid=120400993&loc=SL114874131-224263

Reference 8: http://www.xbrl.org/2003/role/disclosureRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 235
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-05(b)(2))
-URI https://asc.fasb.org/extlink&oid=120399901&loc=d3e537907-122884

Reference 9: http://www.xbrl.org/2003/role/exampleRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 280
-SubTopic 10
-Section 50
-Paragraph 31
-URI https://asc.fasb.org/extlink&oid=126901519&loc=d3e8924-108599

Reference 10: http://fasb.org/us-gaap/role/ref/legacyRef
-Publisher FASB
-Name Accounting Standards Codification
-Topic 942
-SubTopic 220
-Section S99
-Paragraph 1
-Subparagraph (SX 210.9-04(15))
-URI https://asc.fasb.org/extlink&oid=120399700&loc=SL114874048-224260

+ Details

- Definition

Amount of current income tax expense (benefit) and deferred income tax expense (benefit) pertaining to continuing operations.

+ References + Details