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Segments Segments (Sales Based on Customer Location and Property, Plant and Equipment by Geographic Area) (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2023
Oct. 01, 2022
Oct. 02, 2021
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales $ 3,319,122 $ 3,035,783 $ 2,851,993
Property, Plant and Equipment, Net 814,696 668,908 645,778
United States      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 2,152,967 2,041,952 1,935,626
Property, Plant and Equipment, Net 537,908 466,427 438,851
Germany      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 203,666 164,388 148,739
UNITED KINGDOM      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Property, Plant and Equipment, Net 125,471 61,950 62,662
Philippines      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Property, Plant and Equipment, Net 33,559 32,905 35,851
Other (Non-US)      
Revenues from External Customers and Long-Lived Assets [Line Items]      
Net sales 962,489 829,443 767,628
Property, Plant and Equipment, Net $ 117,758 $ 107,626 $ 108,414