Reportable Segments - Financial Information (Details)		3 Months Ended								12 Months Ended
	Jun. 28, 2021 USD ($)	Oct. 03, 2021 USD ($)	Jun. 27, 2021 USD ($)	Mar. 28, 2021 USD ($)	Dec. 27, 2020 USD ($)	Sep. 27, 2020 USD ($)	Jun. 28, 2020 USD ($)	Mar. 29, 2020 USD ($)	Dec. 29, 2019 USD ($)	Oct. 03, 2021 USD ($) segment	Sep. 27, 2020 USD ($)	Sep. 29, 2019 USD ($)
Financial information concerning reportable segments
Number of reportable segments | segment										2
Revenue		$ 892,012,000	$ 801,633,000	$ 754,764,000	$ 765,104,000	$ 753,364,000	$ 709,771,000	$ 734,133,000	$ 797,623,000	$ 3,213,513,000	$ 2,994,891,000	$ 3,107,348,000
Income from operations		81,836,000	$ 69,807,000	$ 60,807,000	$ 66,252,000	66,735,000	$ 63,525,000	$ 47,530,000	$ 63,302,000	278,701,000	241,091,000	188,762,000
Amortization expense for intangible assets										11,500,000	11,600,000	11,600,000
Fair value adjustments to contingent consideration liabilities										3,273,000	14,971,000	(1,085,000)
Impairment of goodwill	$ 0					15,800,000				0	15,800,000	7,755,000
Total assets		2,576,562,000				2,378,558,000				2,576,562,000	2,378,558,000
GSG
Financial information concerning reportable segments
Impairment of goodwill											0
CIG
Financial information concerning reportable segments
Impairment of goodwill											15,800,000
Operating segments | GSG
Financial information concerning reportable segments
Revenue										1,942,958,000	1,778,922,000	1,820,671,000
Income from operations										195,297,000	168,669,000	185,263,000
Total assets		604,366,000				649,417,000				604,366,000	649,417,000
Operating segments | CIG
Financial information concerning reportable segments
Revenue										1,325,668,000	1,266,059,000	1,342,509,000
Income from operations										131,720,000	114,022,000	79,633,000
Total assets		572,607,000				479,238,000				572,607,000	479,238,000
Operating segments | RCM
Financial information concerning reportable segments
Revenue										613,000	198,000	(1,542,000)
Income from operations										0	0	(5,933,000)
Total assets		11,360,000				14,258,000				11,360,000	14,258,000
Elimination of inter-segment revenue
Financial information concerning reportable segments
Revenue										(55,726,000)	(50,288,000)	(54,290,000)
Corporate
Financial information concerning reportable segments
Income from operations										(48,316,000)	(41,600,000)	$ (70,201,000)
Total assets		$ 1,388,229,000				$ 1,235,645,000				$ 1,388,229,000	$ 1,235,645,000