Goodwill and Intangible Assets - Changes in Carrying Value of Goodwill (Details) - USD ($) $ in Thousands	12 Months Ended
	Oct. 02, 2022	Oct. 03, 2021
Goodwill [Roll Forward]
Balance at beginning of the period	$ 1,108,578	$ 993,498
Goodwill reallocation	0
Acquisitions	68,683	90,591
Translation and other	(66,849)	24,489
Balance at end of the period	1,110,412	1,108,578
GSG
Goodwill [Roll Forward]
Balance at beginning of the period	538,433	516,315
Goodwill reallocation	(51,497)
Acquisitions	42,365	15,112
Translation and other	(10,199)	7,006
Balance at end of the period	519,102	538,433
CIG
Goodwill [Roll Forward]
Balance at beginning of the period	570,145	477,183
Goodwill reallocation	51,497
Acquisitions	26,318	75,479
Translation and other	(56,650)	17,483
Balance at end of the period	$ 591,310	$ 570,145