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Reportable Segments (Details) $ in Thousands	3 Months Ended		6 Months Ended
	Apr. 03, 2022 USD ($)	Mar. 28, 2021 USD ($)	Apr. 03, 2022 USD ($) segment	Mar. 28, 2021 USD ($)	Oct. 03, 2021 USD ($)
Segment Reporting Information [Line Items]
Number of reportable segments | segment			2
Revenue	$ 852,744	$ 754,764	$ 1,711,255	$ 1,519,868
Income from operations	74,520	60,807	161,740	127,059
Total Assets	2,645,625		2,645,625		$ 2,576,562
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	448,956	432,570	905,054	857,233
Income from operations	50,344	41,473	101,524	84,169
Total Assets	544,698		544,698		545,533
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	416,945	335,432	833,231	691,958
Income from operations	40,485	30,946	85,792	65,509
Total Assets	743,080		743,080		698,916
Operating segments | RCM
Segment Reporting Information [Line Items]
Revenue	0	470	0	470
Income from operations	0	1	0	1
Total Assets	11,316		11,316		11,360
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(13,157)	(13,708)	(27,030)	(29,793)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(16,309)	$ (11,613)	(25,576)	$ (22,620)
Total Assets	$ 1,346,531		$ 1,346,531		$ 1,320,753

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