Acquisitions - Narrative (Details) £ / shares in Units, $ / shares in Units, $ in Thousands, £ in Millions			3 Months Ended			12 Months Ended
	Jan. 23, 2023 USD ($) employee	Jan. 23, 2023 GBP (£) employee	Mar. 31, 2024 USD ($)	Oct. 01, 2023 USD ($) program	Apr. 02, 2023 USD ($)	Sep. 29, 2024 USD ($)	Oct. 01, 2023 USD ($) program employee $ / shares	Oct. 02, 2022 USD ($) acquisition	Sep. 23, 2022 £ / shares
Business Acquisition [Line Items]
Goodwill				$ 1,880,244		$ 2,046,569	$ 1,880,244	$ 1,110,412
Acquisition and integration expenses						7,138	33,169	0
(Loss) gain in contingent earn-out liabilities						$ (2,500)	(12,300)	(300)
Minimum
Business Acquisition [Line Items]
Earn-out period						3 years
Useful life of intangible assets						1 year
Significant unobservable input, earn-out period						3 years
Maximum
Business Acquisition [Line Items]
Earn-out period						5 years
Useful life of intangible assets						12 years
Significant unobservable input, earn-out period						5 years
LS Technologies
Business Acquisition [Line Items]
Fair value of acquisition purchase price			$ 120,000
Initial cash payments			93,000
Cash holdback related to tax reserve			4,000
Equity interests issued and issuable			23,000
Net tangible assets			12,000
Intangible assets			23,000
Goodwill			85,000
LS Technologies | Maximum
Business Acquisition [Line Items]
Equity interests issued and issuable			$ 60,000
RPS Group PLC
Business Acquisition [Line Items]
Fair value of acquisition purchase price	$ 784,000	£ 633
Intangible assets	174,094
Goodwill	$ 652,762
Price of acquisition, expected, per share (in pounds per share) | £ / shares									£ 2.22
Number of employees (over for Amyx) | employee	5,000	5,000
Acquisition and integration expenses				$ 7,300	$ 19,900		33,200
Net purchase price	$ 675,000
Revenue							600,000
Net income (loss)							$ 3,600
Diluted earnings per share (in dollars per share) | $ / shares							$ 0.01
Intangible amortization							$ 26,800
RPS Group PLC | Foreign Exchange Contract
Business Acquisition [Line Items]
Foreign currency forward contract, asset fair value	$ 109,300
Amyx, Inc.
Business Acquisition [Line Items]
Fair value of acquisition purchase price							$ 120,900
Number of employees (over for Amyx) | employee							500
Number of government programs acquired (over) | program				30			30
Promissory note							$ 100,000
Payables (receivables) related to estimated post-closing adjustments							8,700
Contingent earn-out liability				$ 12,200			12,200
Aggregate maximum of contingent consideration				$ 25,000			$ 25,000
Business acquisitions
Business Acquisition [Line Items]
Fair value of acquisition purchase price								88,300
Initial cash payments								44,000
Promissory note								15,500
Payables (receivables) related to estimated post-closing adjustments								(2,500)
Contingent earn-out liability								31,300
Aggregate maximum of contingent consideration								$ 47,000
Number of acquisitions | acquisition								4
Business acquisitions | Minimum
Business Acquisition [Line Items]
Earn-out period								3 years
Business acquisitions | Maximum
Business Acquisition [Line Items]
Earn-out period								5 years