Reportable Segments - Financial Information (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 28, 2021 USD ($)	Mar. 29, 2020 USD ($)	Mar. 28, 2021 USD ($) segment	Mar. 29, 2020 USD ($)	Sep. 27, 2020 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment			2
Revenue	$ 754,764	$ 734,133	$ 1,519,868	$ 1,531,756
Income from operations	60,807	47,530	127,059	110,832
Total Assets	2,455,062		2,455,062		$ 2,378,558
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	473,829	436,903	942,451	894,307
Income from operations	46,109	35,347	93,809	77,395
Total Assets	635,217		635,217		649,417
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	293,128	308,412	604,152	659,576
Income from operations	26,311	21,676	55,869	53,309
Total Assets	463,176		463,176		479,238
Operating segments | RCM
Segment Reporting Information [Line Items]
Revenue	470	5	470	150
Income from operations	1	(1)	1	1
Total Assets	11,369		11,369		14,258
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(12,663)	(11,187)	(27,205)	(22,277)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(11,614)	$ (9,492)	(22,620)	$ (19,873)
Total Assets	$ 1,345,300		$ 1,345,300		$ 1,235,645