Reportable Segments (Details) $ in Thousands	3 Months Ended
	Jan. 02, 2022 USD ($) segment	Dec. 27, 2020 USD ($)	Oct. 03, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment	2
Revenue	$ 858,510	$ 765,104
Income from operations	87,220	66,252
Total Assets	2,640,456		$ 2,576,562
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	456,099	424,663
Income from operations	51,179	42,695
Total Assets	575,206		545,533
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	416,286	356,526
Income from operations	45,308	34,563
Total Assets	703,777		698,916
Operating segments | RCM
Segment Reporting Information [Line Items]
Total Assets	11,316		11,360
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(13,875)	(16,085)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(9,267)	$ (11,006)
Total Assets	$ 1,350,157		$ 1,320,753