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Stock Repurchases (Details) - USD ($)
12 Months Ended
Oct. 02, 2021
Oct. 03, 2020
Feb. 05, 2020
Oct. 28, 2018
Oct 2018 repurchase program        
Equity, Class of Treasury Stock [Line Items]        
Authorized repurchase of common stock       $ 250,000,000
Repurchase limit per quarter       $ 75,000,000
Number of shares of outstanding common stock repurchased and retired (shares)   603,828    
Stock repurchase, price paid per share (dollars per share)   $ 128.20    
Total cost of stock repurchased, net   $ 77,400,000    
Feb 2020 repurchase program        
Equity, Class of Treasury Stock [Line Items]        
Authorized repurchase of common stock     $ 100,000,000  
Stock repurchased , value $ 0 $ 0