Segments Segments (Sales Based on Customer Location and Property, Plant and Equipment by Geographic Area) (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 01, 2022	Oct. 02, 2021	Oct. 03, 2020
Revenues from External Customers and Long-Lived Assets [Line Items]
Net sales	$ 3,035,783	$ 2,851,993	$ 2,884,554
Property, Plant and Equipment, Net	668,908	645,778	600,498
United States
Revenues from External Customers and Long-Lived Assets [Line Items]
Net sales	2,041,952	1,935,626	1,873,667
Property, Plant and Equipment, Net	466,427	438,851	389,454
Germany
Revenues from External Customers and Long-Lived Assets [Line Items]
Net sales	164,388	148,739	175,598
Japan
Revenues from External Customers and Long-Lived Assets [Line Items]
Net sales	87,435	108,813	159,025
UNITED KINGDOM
Revenues from External Customers and Long-Lived Assets [Line Items]
Property, Plant and Equipment, Net	61,950	62,662	58,888
Philippines
Revenues from External Customers and Long-Lived Assets [Line Items]
Property, Plant and Equipment, Net	32,905	35,851	37,270
Other (Non-US)
Revenues from External Customers and Long-Lived Assets [Line Items]
Net sales	742,008	658,815	676,264
Property, Plant and Equipment, Net	$ 107,626	$ 108,414	$ 114,886