Reportable Segments (Details) $ in Thousands	3 Months Ended		9 Months Ended
	Jul. 03, 2022 USD ($)	Jun. 27, 2021 USD ($)	Jul. 03, 2022 USD ($) segment	Jun. 27, 2021 USD ($)	Oct. 03, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment			2
Revenue	$ 890,231	$ 801,633	$ 2,601,485	$ 2,321,500
Income from operations	83,905	69,807	245,645	196,865
Total Assets	2,677,706		2,677,706		$ 2,576,562
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	459,987	444,263	1,365,041	1,301,497
Income from operations	45,580	44,323	147,104	128,491
Total Assets	549,648		549,648		545,533
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	444,238	372,722	1,277,469	1,064,680
Income from operations	53,535	38,991	139,328	104,500
Total Assets	756,195		756,195		698,916
Operating segments | RCM
Segment Reporting Information [Line Items]
Revenue	0	143	0	613
Total Assets	2		2		11,360
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(13,994)	(15,495)	(41,025)	(45,290)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(15,210)	$ (13,507)	(40,787)	$ (36,126)
Total Assets	$ 1,371,861		$ 1,371,861		$ 1,320,753