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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 |  |  |

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