Reportable Segments - Summary of Reportable Segments (Details) - USD ($) $ in Thousands	3 Months Ended		6 Months Ended
	Mar. 31, 2024	Apr. 02, 2023	Mar. 31, 2024	Apr. 02, 2023	Oct. 01, 2023
Segment Reporting Information [Line Items]
Revenue	$ 1,251,616	$ 1,158,226	$ 2,479,883	$ 2,052,991
Income from operations	117,683	61,011	228,764	153,061
Total Assets	4,070,574		4,070,574		$ 3,820,477
Operating segments | GSG
Segment Reporting Information [Line Items]
Revenue	597,127	563,254	1,172,168	1,034,322
Income from operations	64,007	52,210	127,134	112,557
Total Assets	628,814		628,814		543,066
Operating segments | CIG
Segment Reporting Information [Line Items]
Revenue	671,155	610,358	1,340,262	1,049,914
Income from operations	75,955	52,518	147,356	102,626
Total Assets	1,045,575		1,045,575		994,470
Elimination of inter-segment revenue
Segment Reporting Information [Line Items]
Revenue	(16,666)	(15,386)	(32,547)	(31,245)
Corporate
Segment Reporting Information [Line Items]
Income from operations	(22,279)	$ (43,717)	(45,726)	$ (62,122)
Total Assets	$ 2,396,185		$ 2,396,185		$ 2,282,941