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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
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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

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