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Employee Stock Purchase and Stock Incentive Plans - Stock Purchase and Stock Option Plans Information on the 1999 Plans (Details) - shares
12 Months Ended
Sep. 30, 2022
Oct. 01, 2021
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Number of shares authorized (in shares) 30,950,000  
Number of remaining shares reserved for issuance (in shares) 4,487,176  
Number of shares relating to outstanding stock options at September 27, 2019 (in shares) 439,349  
Number of shares available for future awards (in shares) 4,047,827 4,354,529
1999 SIP    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Number of shares authorized (in shares) 29,850,000  
Number of remaining shares reserved for issuance (in shares) 4,244,964  
Number of shares relating to outstanding stock options at September 27, 2019 (in shares) 358,224  
Number of shares available for future awards (in shares) 3,886,740 4,166,975
1999 SIP | Other Than Option Stock Appreciation Rights SARS    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Award number of shares, fungible share basis (in shares) 1.92  
Award number of shares, non-fungible share basis (in shares) 1  
1999 ODSP    
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]    
Number of shares authorized (in shares) 1,100,000  
Number of remaining shares reserved for issuance (in shares) 242,212  
Number of shares relating to outstanding stock options at September 27, 2019 (in shares) 81,125  
Number of shares available for future awards (in shares) 161,087 187,554
Award number of shares, non-fungible share basis (in shares) 1.92