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Retirement Plans - Narrative (Details) - USD ($)
$ in Millions
12 Months Ended
Oct. 02, 2022
Oct. 03, 2021
Sep. 27, 2020
Retirement Benefits [Abstract]      
Employer contributions to the plans $ 29.3 $ 26.9 $ 25.0
Assets related to deferred compensation plans 36.7 41.4  
Liabilities related to deferred compensation plans $ 36.3 $ 41.1  
Maximum age pension plan was open for new entrants 24 years    
Defined benefit plan, benefits paid during period $ 1.0