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Shareholders' Equity - Narrative (Details) - USD ($)
 12 Months Ended
Sep. 29, 2018
Sep. 30, 2017
Oct. 01, 2016
Feb. 14, 2018
Jun. 06, 2016
Aug. 20, 2015
Equity, Class of Treasury Stock [Line Items]            
Authorized repurchase amount           $ 30,000,000.0
Amount repurchased (in shares)     760,903      
Amount repurchased $ 137,034,000 $ 34,136,000 $ 30,000,000      
Average repurchase price (in dollars per share)     $ 39.43      
2018 Stock Repurchase Program [Member]            
Equity, Class of Treasury Stock [Line Items]            
Authorized repurchase amount       $ 200,000,000.0    
Amount repurchased (in shares) 343,642          
Amount repurchased $ 21,200,000          
Average repurchase price (in dollars per share) $ 61.61          
Stock Repurchase Program, Remaining Authorized Repurchase Amount $ 178,800,000          
2016 Stock Repurchase Program            
Equity, Class of Treasury Stock [Line Items]            
Authorized repurchase amount         $ 150,000,000  
Amount repurchased (in shares) 1,914,596 655,470        
Amount repurchased $ 115,900,000 $ 34,100,000        
Average repurchase price (in dollars per share) $ 60.52 $ 52.08