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Derivative Financial Instruments (Details)
$ in Thousands, £ in Millions
3 Months Ended 12 Months Ended
Apr. 02, 2023
USD ($)
Jan. 01, 2023
USD ($)
Sep. 28, 2025
USD ($)
Sep. 29, 2024
USD ($)
Oct. 01, 2023
USD ($)
Sep. 30, 2018
agreement
Jan. 23, 2023
USD ($)
Dec. 28, 2022
USD ($)
Dec. 28, 2022
GBP (£)
Oct. 02, 2022
USD ($)
Oct. 02, 2022
GBP (£)
Derivative [Line Items]                      
Other non-operating income     $ 0 $ 0 $ 89,402            
Loss on cash flow hedge valuations, net of tax     $ 0 $ 0 $ 2,412            
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    
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                  
Interest Rate Swap | Cash flow hedges | Derivatives designated as hedging instruments                      
Derivative [Line Items]                      
Number of derivative agreements | agreement           5