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Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($)
$ in Thousands
Jun. 29, 2024
Sep. 30, 2023
Jun. 24, 2023
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross $ 737,900 $ 737,800 $ 737,800
Accumulated Amortization (223,800) (199,400) (191,200)
Accumulated Impairment (41,200) (41,200) (34,500)
Net Carrying Value 472,854 497,228 512,175
Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 274,700 274,600 274,600
Accumulated Amortization (22,000) (21,500) (21,300)
Accumulated Impairment (29,400) (29,400) (26,000)
Net Carrying Value 223,200 223,700 227,300
Other acquired intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 46,800 46,800 46,800
Accumulated Amortization (33,400) (30,500) (29,500)
Accumulated Impairment (1,500) (1,500) (1,200)
Net Carrying Value 11,900 14,800 16,100
Amortizable | Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 22,100 22,100 22,100
Accumulated Amortization (22,000) (21,500) (21,300)
Accumulated Impairment 0 0 0
Net Carrying Value 100 600 800
Amortizable | Customer-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 416,400 416,400 416,400
Accumulated Amortization (168,400) (147,400) (140,300)
Accumulated Impairment (10,300) (10,300) (7,300)
Net Carrying Value 237,700 258,800 268,800
Amortizable | Other acquired intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 39,700 39,700 39,700
Accumulated Amortization (33,400) (30,500) (29,500)
Accumulated Impairment (300) (300) 0
Net Carrying Value 6,000 8,900 10,200
Nonamortizable | Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 252,500 252,500 252,500
Accumulated Amortization 0 0 0
Accumulated Impairment (29,400) (29,400) (26,000)
Net Carrying Value 223,100 223,100 226,500
Nonamortizable | Other acquired intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 7,100 7,100 7,100
Accumulated Amortization 0 0 0
Accumulated Impairment (1,200) (1,200) (1,200)
Net Carrying Value $ 5,900 $ 5,900 $ 5,900