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Pension and Other Postretirement Benefit Plans - Narrative (Details) - USD ($)
$ in Thousands
 3 Months Ended 12 Months Ended
Jul. 02, 2021
Sep. 30, 2022
Oct. 01, 2021
Oct. 02, 2020
Mar. 02, 2021
Defined Benefit Plan Disclosure [Line Items]          
Loss on pension and retiree medical plan changes   $ 123 $ 2,783 $ 4,598  
Gain on litigation settlement   $ 19,500      
Pension Plan          
Defined Benefit Plan Disclosure [Line Items]          
Period of annual average returns used in return on plan assets simulation model (in years)   20 years      
PA Consulting Group Limited          
Defined Benefit Plan Disclosure [Line Items]          
Percentage of outstanding shares of common and preferred stock acquired         65.00%
PA Consulting | Pension Plan          
Defined Benefit Plan Disclosure [Line Items]          
Net benefit obligation at the end of the year         $ 1,025,000
Fair value of plan assets at the end of the year         $ 1,018,000
Plan assets (decrease) for assets transferred from Plan $ 960,000        
Benefit obligation decrease for liabilities transferred from plan $ 960,000        
Sverdrup and Ireland Pension Plans | Pension Plan          
Defined Benefit Plan Disclosure [Line Items]          
Loss on pension and retiree medical plan changes   $ 100 $ 2,800