Reportable Segments - Financial Information (Details) - USD ($) $ in Thousands	3 Months Ended								12 Months Ended
	Sep. 29, 2024	Jun. 30, 2024	Mar. 31, 2024	Dec. 31, 2023	Oct. 01, 2023	Jul. 02, 2023	Apr. 02, 2023	Jan. 01, 2023	Sep. 29, 2024	Oct. 01, 2023	Oct. 02, 2022
Financial information concerning reportable segments
Revenue	$ 1,374,473	$ 1,344,323	$ 1,251,616	$ 1,228,267	$ 1,260,611	$ 1,208,947	$ 1,158,226	$ 894,766	$ 5,198,679	$ 4,522,550	$ 3,504,048
Income from operations	143,343	$ 128,630	$ 117,683	$ 111,081	107,377	$ 97,675	$ 61,011	$ 92,050	500,737	358,113	340,446
Amortization expense for intangible assets									50,000	41,200	13,200
(Loss) income for fair value adjustments									(2,500)	(12,300)	(300)
Total assets	4,192,676				3,820,477				4,192,676	3,820,477
Operating segments | GSG
Financial information concerning reportable segments
Revenue									2,483,355	2,158,889	1,820,868
Income from operations									281,026	231,762	198,448
Total assets	658,493				543,066				658,493	543,066
Operating segments | CIG
Financial information concerning reportable segments
Revenue									2,786,731	2,424,649	1,738,436
Income from operations									328,510	243,750	194,142
Total assets	1,059,915				994,470				1,059,915	994,470
Elimination of inter-segment revenue
Financial information concerning reportable segments
Revenue									(71,407)	(60,988)	(55,256)
Corporate
Financial information concerning reportable segments
Income from operations									(108,799)	(117,399)	$ (52,144)
Total assets	$ 2,474,268				$ 2,282,941				$ 2,474,268	$ 2,282,941