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Share-Based Compensation - Fair Value Assumptions (Details) - Options - $ / shares
12 Months Ended
Oct. 02, 2021
Oct. 03, 2020
Sep. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected volatility 41.00% 32.00% 31.00%
Expected dividend yield 0.00% 0.00% 0.00%
Risk-free interest rate 0.49% 1.61% 2.75%
Weighted-average grant-date fair value (in dollars per share) $ 6.58 $ 6.91 $ 5.58
Minimum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected term (in years) 2 years 8 months 12 days 4 years 6 months 4 years 6 months
Maximum      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Expected term (in years) 6 years 6 years 5 years 6 months