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Share-Based Compensation - Narrative (Details) - USD ($)
$ / shares in Units, $ in Millions
12 Months Ended
Oct. 02, 2021
Oct. 03, 2020
Sep. 28, 2019
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Shares authorized to be granted under Omnibus Equity Incentive Plan (in shares) 5,200,000    
Exercise price as a percentage of fair value 100.00%    
Stock-based compensation $ 1.9 $ 1.4 $ 1.5
Tax benefit from compensation expense $ 0.5 0.4 0.4
Unrecognized compensation expense, period for recognition 9 months    
Aggregate intrinsic value of options exercised during period $ 1.1 $ 4.3 $ 0.1
Unrecognized compensation costs $ 0.8    
Restricted Stock and Restricted Stock Units (RSUs)      
Share-based Compensation Arrangement by Share-based Payment Award [Line Items]      
Weighted-average grant date fair value of restricted stock awards (in dollars per share) $ 18.82 $ 18.64 $ 17.30
Stock-based compensation $ 3.9 $ 2.7 $ 2.6
Tax benefit from compensation expense 1.0 $ 0.7 $ 0.7
Unrecognized compensation expense $ 1.3    
Unrecognized compensation expense, period for recognition 9 months