GOODWILL AND INTANGIBLE ASSETS - NET - Summary of Finite-Lived Intangible Assets (Detail) - USD ($) $ in Thousands	Sep. 30, 2024	Sep. 30, 2023
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	$ 687,248	$ 720,068
Accumulated Amortization	(532,730)	(520,571)
Net Carrying Value	154,518	199,497
Propriety knowledge
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	300,490	300,400
Accumulated Amortization	(268,358)	(253,608)
Net Carrying Value	32,132	46,792
Trademarks
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	217,730	230,240
Accumulated Amortization	(167,015)	(164,759)
Net Carrying Value	50,715	65,481
Customer relationships
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	156,452	176,852
Accumulated Amortization	(86,600)	(92,268)
Net Carrying Value	69,852	84,584
Patents
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	8,500	8,500
Accumulated Amortization	(6,715)	(5,913)
Net Carrying Value	1,785	2,587
Other intangible assets
Finite Lived Intangible Assets [Line Items]
Gross Carrying Value	4,076	4,076
Accumulated Amortization	(4,042)	(4,023)
Net Carrying Value	$ 34	$ 53
Minimum
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	3 years
Minimum | Propriety knowledge
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	10 years	10 years
Minimum | Trademarks
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	5 years	5 years
Minimum | Customer relationships
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	12 years	12 years
Minimum | Patents
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	9 years	9 years
Minimum | Other intangible assets
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	3 years	3 years
Maximum
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	20 years
Maximum | Propriety knowledge
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	15 years	15 years
Maximum | Trademarks
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	20 years	20 years
Maximum | Customer relationships
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	19 years	19 years
Maximum | Patents
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	10 years	10 years
Maximum | Other intangible assets
Finite Lived Intangible Assets [Line Items]
Acquired finite lived intangible asset useful life	15 years	15 years