Goodwill and Intangible Assets - Goodwill (Details) $ in Thousands	3 Months Ended
	Jan. 01, 2023 USD ($)
Goodwill
Balance at beginning of the period	$ 1,110,412
Translation adjustments	22,891
Balance at end of the period	1,133,303
GSG
Goodwill
Balance at beginning of the period	519,102
Translation adjustments	2,792
Balance at end of the period	521,894
CIG
Goodwill
Balance at beginning of the period	591,310
Translation adjustments	20,099
Balance at end of the period	$ 611,409