Acquisitions - Narrative (Details) £ / shares in Units, $ / shares in Units, $ in Thousands, £ in Millions			3 Months Ended		9 Months Ended	12 Months Ended
	Jan. 23, 2023 USD ($) employee	Jan. 23, 2023 GBP (£) employee	Oct. 01, 2023 USD ($) program	Apr. 02, 2023 USD ($)	Jul. 02, 2023 USD ($)	Oct. 01, 2023 USD ($) program employee $ / shares	Oct. 02, 2022 USD ($) acquisition	Oct. 03, 2021 USD ($)	Sep. 23, 2022 £ / shares
Business Acquisition [Line Items]
Acquisition and integration expenses						$ 33,169	$ 0	$ 0
Contingent earn-out liability			$ 73,400			73,400
Number of acquisitions | acquisition							4
(Loss) gain in contingent earn-out liabilities						$ (12,300)	$ (300)	$ 3,300
Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]						Foreign currency translation adjustments, net of tax	Foreign currency translation adjustments, net of tax	Foreign currency translation adjustments, net of tax
Interest expense | Contingent consideration
Business Acquisition [Line Items]
Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]						Interest Expense	Interest Expense	Interest Expense
Operating income | Contingent consideration
Business Acquisition [Line Items]
Fair Value, Liability, Recurring Basis, Unobservable Input Reconciliation, Gain (Loss), Statement of Income or Comprehensive Income [Extensible Enumeration]						Income from operations	Income from operations	Income from operations
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
Trade names
Business Acquisition [Line Items]
Useful life of intangible assets						2 years 4 months 24 days
RPS Group PLC
Business Acquisition [Line Items]
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	$ 33,200
Net purchase price	$ 675,000
Revenue						600,000
Net income (loss)						$ 3,600
Diluted earnings per share (in dollars per share) | $ / shares						$ 0.07
Intangible amortization						$ 26,800
Fair value of acquisition purchase price	$ 784,000	£ 633
Useful life of intangible assets	8 years 3 months 18 days	8 years 3 months 18 days
RPS Group PLC | Foreign Exchange Contract
Business Acquisition [Line Items]
Foreign currency forward contract, asset fair value	$ 109,300
RPS Group PLC | Trade names
Business Acquisition [Line Items]
Useful life of intangible assets	3 years	3 years
Amyx, Inc.
Business Acquisition [Line Items]
Number of employees (over for Amyx) | employee						500
Number of government programs acquired (over) | program			30			30
Fair value of acquisition purchase price						$ 120,900
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
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
Initial cash payments							$ 44,000
Business acquisitions | Minimum
Business Acquisition [Line Items]
Earn-out period							3 years
Business acquisitions | Maximum
Business Acquisition [Line Items]
Earn-out period							5 years
All acquisitions
Business Acquisition [Line Items]
Aggregate maximum of contingent consideration			$ 113,800			$ 113,800