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Derivative Financial Instruments - Narrative (Details) $ in Thousands, £ in Millions | 3 Months Ended | 12 Months Ended |  |  |
--- | --- | --- | --- | --- | ---
Apr. 02, 2023 USD ($) | Jan. 01, 2023 USD ($) | Sep. 29, 2024 USD ($) | Oct. 01, 2023 USD ($) | Oct. 02, 2022 USD ($) | Sep. 30, 2018 agreement | Jan. 23, 2023 USD ($) | Dec. 28, 2022 USD ($) | Dec. 28, 2022 GBP (£) | Oct. 02, 2022 GBP (£)
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Other non-operating income |  |  | $ 0 | $ 89,402 | $ 19,904 |  |  |  |  |
(Loss) gain on cash flow hedge valuations, net of tax |  |  | $ 0 | $ (2,412) | $ 11,806 |  |  |  |  |
RPS Group plc |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Derivative, forward exchange rate |  |  |  |  | 1.0852 |  |  |  |  | 1.0852
RPS Group PLC |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Derivative, forward exchange rate |  |  |  |  |  |  |  | 1.086 | 1.086 |
Interest Rate Swap | Cash flow hedges | Derivatives designated as hedging instruments |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Number of derivative agreements | agreement |  |  |  |  |  | 5 |  |  |  |
Fair value of interest rate swap agreements |  |  |  |  | $ 2,400 |  |  |  |  |
Foreign Exchange Contract | RPS Group plc |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  |  |  |  | 774,800 |  |  |  |  | £ 714.0
Foreign currency forward contract, asset fair value |  |  |  |  | $ 19,900 |  |  |  |  |
Foreign Exchange Contract | RPS Group PLC |  |  |  |  |  |  |  |  |  |
Derivative [Line Items] |  |  |  |  |  |  |  |  |  |
Notional amount |  |  |  |  |  |  |  | $ 775,400 | £ 714.0 |
Foreign currency forward contract, asset fair value |  |  |  |  |  |  | $ 109,300 |  |  |
Other non-operating income | $ 21,400 | $ 68,000 |  |  |  |  |  |  |  |

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