Reportable Segments - Financial Information (Details)		3 Months Ended								12 Months Ended
	Jun. 29, 2020 USD ($)	Sep. 27, 2020 USD ($)	Jun. 28, 2020 USD ($)	Mar. 29, 2020 USD ($)	Dec. 29, 2019 USD ($)	Sep. 29, 2019 USD ($)	Jun. 30, 2019 USD ($)	Mar. 31, 2019 USD ($)	Dec. 30, 2018 USD ($)	Sep. 27, 2020 USD ($) segment	Sep. 29, 2019 USD ($)	Sep. 30, 2018 USD ($)
Financial information concerning reportable segments
Number of reportable segments | segment										2
Revenue		$ 753,364,000	$ 709,771,000	$ 734,133,000	$ 797,623,000	$ 841,502,000	$ 825,793,000	$ 722,621,000	$ 717,431,000	$ 2,994,891,000	$ 3,107,348,000	$ 2,964,148,000
Income from operations		66,735,000	$ 63,525,000	$ 47,530,000	$ 63,302,000	20,665,000	$ 64,841,000	$ 47,545,000	$ 55,711,000	241,091,000	188,762,000	190,086,000
Amortization expense for intangible assets										11,600,000	11,600,000	18,200,000
Fair value adjustments to contingent consideration liabilities										14,971,000	(1,085,000)	(4,252,000)
Impairment of goodwill	$ 0	15,800,000				7,800,000				15,800,000	7,755,000	0
Total Assets		2,378,558,000				2,147,408,000				2,378,558,000	2,147,408,000
GSG
Financial information concerning reportable segments
Impairment of goodwill										0	0
CIG
Financial information concerning reportable segments
Impairment of goodwill										15,800,000	7,755,000
Operating segments | GSG
Financial information concerning reportable segments
Revenue										1,778,922,000	1,820,671,000	1,694,871,000
Income from operations										168,669,000	185,263,000	168,211,000
Total Assets		649,417,000				587,040,000				649,417,000	587,040,000
Operating segments | CIG
Financial information concerning reportable segments
Revenue										1,266,059,000	1,342,509,000	1,323,142,000
Income from operations										114,022,000	79,633,000	74,451,000
Total Assets		479,238,000				450,276,000				479,238,000	450,276,000
Operating segments | RCM
Financial information concerning reportable segments
Revenue										198,000	(1,542,000)	14,199,000
Income from operations										0	(5,933,000)	(4,573,000)
Total Assets		14,258,000				15,608,000				14,258,000	15,608,000
Elimination of inter-segment revenue
Financial information concerning reportable segments
Revenue										(50,288,000)	(54,290,000)	(68,064,000)
Corporate
Financial information concerning reportable segments
Income from operations										(41,600,000)	(70,201,000)	$ (48,003,000)
Total Assets		$ 1,235,645,000				$ 1,094,484,000				$ 1,235,645,000	$ 1,094,484,000