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Other Intangible Assets - Components of Gross and Net Acquired Intangible Assets (Details) - USD ($)
$ in Thousands
Mar. 29, 2025
Sep. 28, 2024
Mar. 30, 2024
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross $ 763,000 $ 760,800 $ 737,800
Accumulated Amortization (247,400) (233,500) (215,700)
Accumulated Impairment (54,000) (54,000) (41,200)
Net Carrying Value 461,657 473,280 480,910
Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 292,300 292,300 274,600
Accumulated Amortization (23,100) (22,800) (21,900)
Accumulated Impairment (35,000) (35,000) (29,400)
Net Carrying Value 234,300 234,500 223,300
Other acquired intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 49,100 46,800 46,800
Accumulated Amortization (35,400) (34,300) (32,500)
Accumulated Impairment (1,500) (1,500) (1,500)
Net Carrying Value 12,200 11,000 12,800
Amortizable | Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 26,000 26,000 22,100
Accumulated Amortization (23,100) (22,800) (21,900)
Accumulated Impairment 0 0 0
Net Carrying Value 2,900 3,100 200
Amortizable | Customer-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 421,700 421,700 416,400
Accumulated Amortization (188,900) (176,400) (161,400)
Accumulated Impairment (17,500) (17,500) (10,300)
Net Carrying Value 215,200 227,800 244,700
Amortizable | Other acquired intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 41,900 39,700 39,700
Accumulated Amortization (35,400) (34,300) (32,500)
Accumulated Impairment (300) (300) (300)
Net Carrying Value 6,300 5,100 6,900
Nonamortizable | Marketing-related intangible assets      
Acquired Indefinite-lived Intangible Assets [Line Items]      
Gross 266,300 266,300 252,500
Accumulated Amortization 0 0 0
Accumulated Impairment (35,000) (35,000) (29,400)
Net Carrying Value 231,400 231,400 223,100
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