Reportable Segments (Details) $ in Thousands	3 Months Ended
	Jan. 01, 2023 USD ($) segment	Jan. 02, 2022 USD ($)	Oct. 02, 2022 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment	2
Revenue	$ 894,766	$ 858,510
Income from operations	92,050	87,220
Total Assets	2,731,480		$ 2,622,776
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	471,067	456,099
Income from operations	60,347	51,179
Total Assets	586,128		558,764
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	439,556	416,286
Income from operations	50,108	45,308
Total Assets	742,288		688,640
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(15,857)	(13,875)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(18,405)	$ (9,267)
Total Assets	$ 1,403,064		$ 1,375,372