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Goodwill and Other Intangible Assets - Schedule of Goodwill Assets by Segment (Details)
$ in Thousands
 3 Months Ended
Dec. 29, 2023
USD ($)
Goodwill [Roll Forward]  
Balance at beginning of the period $ 4,615,986
Acquisitions 29,057
Translation 15,975
Balance at the end of the period 4,661,018
FSS - United States  
Goodwill [Roll Forward]  
Balance at beginning of the period 4,164,392
Acquisitions 24,159
Translation 58
Balance at the end of the period 4,188,609
FSS International  
Goodwill [Roll Forward]  
Balance at beginning of the period 451,594
Acquisitions 4,898
Translation 15,917
Balance at the end of the period $ 472,409