Reportable Segments - Financial Information (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Oct. 01, 2023	Jul. 02, 2023	Apr. 02, 2023	Jan. 01, 2023	Oct. 02, 2022	Jul. 03, 2022	Apr. 03, 2022	Jan. 02, 2022	Oct. 01, 2023	Oct. 02, 2022	Oct. 03, 2021
Financial information concerning reportable segments
Revenue	$ 1,260,611	$ 1,208,947	$ 1,158,226	$ 894,766	$ 902,562	$ 890,231	$ 852,744	$ 858,510	$ 4,522,550	$ 3,504,048	$ 3,213,513
Income from operations	107,377	$ 97,675	$ 61,011	$ 92,050	94,802	$ 83,905	$ 74,520	$ 87,220	358,113	340,446	278,701
Amortization expense for intangible assets									41,200	13,200	11,500
(Loss) income for fair value adjustments									(12,300)	(300)	3,300
Total assets	3,820,477				2,622,776				3,820,477	2,622,776
Operating segments | GSG
Financial information concerning reportable segments
Revenue									2,158,889	1,820,868	1,772,905
Income from operations									231,762	198,448	174,755
Total assets	543,066				558,764				543,066	558,764
Operating segments | CIG
Financial information concerning reportable segments
Revenue									2,424,649	1,738,436	1,500,074
Income from operations									243,750	194,142	152,262
Total assets	994,470				688,640				994,470	688,640
Elimination of inter-segment revenue
Financial information concerning reportable segments
Revenue									(60,988)	(55,256)	(59,466)
Corporate
Financial information concerning reportable segments
Income from operations									(117,399)	(52,144)	$ (48,316)
Total assets	$ 2,282,941				$ 1,375,372				$ 2,282,941	$ 1,375,372