Reportable Segments - Financial Information (Details)		3 Months Ended								12 Months Ended
	Jul. 04, 2022 USD ($)	Oct. 02, 2022 USD ($)	Jul. 03, 2022 USD ($)	Apr. 03, 2022 USD ($)	Jan. 02, 2022 USD ($)	Oct. 03, 2021 USD ($)	Jun. 27, 2021 USD ($)	Mar. 28, 2021 USD ($)	Dec. 27, 2020 USD ($)	Oct. 02, 2022 USD ($) segment	Oct. 03, 2021 USD ($)	Sep. 27, 2020 USD ($)
Financial information concerning reportable segments
Number of reportable segments | segment										2
Revenue		$ 902,562,000	$ 890,231,000	$ 852,744,000	$ 858,510,000	$ 892,012,000	$ 801,633,000	$ 754,764,000	$ 765,104,000	$ 3,504,048,000	$ 3,213,513,000	$ 2,994,891,000
Income from operations		94,802,000	$ 83,905,000	$ 74,520,000	$ 87,220,000	81,836,000	$ 69,807,000	$ 60,807,000	$ 66,252,000	340,446,000	278,701,000	241,091,000
Amortization expense for intangible assets										13,200,000	11,500,000	11,600,000
Fair value adjustments to contingent consideration liabilities										(329,000)	3,273,000	14,971,000
Impairment of goodwill	$ 0									0	0	15,800,000
Total assets		2,622,776,000				2,576,562,000				2,622,776,000	2,576,562,000
Operating segments | GSG
Financial information concerning reportable segments
Revenue										1,820,868,000	1,772,905,000	1,578,332,000
Income from operations										198,448,000	174,755,000	146,273,000
Total assets		558,764,000				545,533,000				558,764,000	545,533,000
Operating segments | CIG
Financial information concerning reportable segments
Revenue										1,738,436,000	1,500,074,000	1,471,097,000
Income from operations										194,142,000	152,262,000	136,418,000
Total assets		688,640,000				698,916,000				688,640,000	698,916,000
Operating segments | RCM
Financial information concerning reportable segments
Revenue										0	613,000	198,000
Total assets		2,000				11,360,000				2,000	11,360,000
Elimination of inter-segment revenue
Financial information concerning reportable segments
Revenue										(55,256,000)	(60,079,000)	(54,736,000)
Corporate
Financial information concerning reportable segments
Income from operations										(52,144,000)	(48,316,000)	$ (41,600,000)
Total assets		$ 1,375,370,000				$ 1,320,753,000				$ 1,375,370,000	$ 1,320,753,000