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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details) $ in Thousands | 3 Months Ended | 9 Months Ended |
--- | --- | --- | ---
Jun. 28, 2024 USD ($) country | Jun. 30, 2023 USD ($) | Jun. 28, 2024 USD ($) segment country | Jun. 30, 2023 USD ($) | Sep. 29, 2023 USD ($)
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Number of reportable segments | segment |  |  | 2 |  |
Pension plan adjustments from spin-off |  |  | $ 5,100 |  |
Foreign currency translation adjustments, spin-off |  |  | 26,300 |  |
Cash and cash equivalents | $ 436,075 | $ 388,166 | 436,075 | $ 388,166 | $ 1,927,088
Impairment charges |  |  | 0 | 27,781 |
Equity method investment, aggregate cost | 75,400 |  | 75,400 |  | 73,500
Pre-tax gain (loss) on sale of equity investment |  | 1,100 |  | 1,100 |
Equity securities without readily determinable fair value, amount | 83,600 |  | 83,600 |  | 83,600
Proceeds from sale of equity investments |  | 98,200 | 0 | 633,179 |
Loss on sale of equity investment, net of tax |  | 2,200 |  | 2,200 |
Supplier finance program, obligation | 2,900 |  | 2,900 |  | 2,800
Payment of deferred social security taxes |  |  |  | 47,600 |
Equity Method Investments |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Pre-tax gain (loss) on sale of equity investment |  | (377,100) |  | (377,100) |
Gain on sale of this equity investment |  | $ 275,900 |  | $ 275,900 |
AIM Services Co., Ltd | AIM Services Co., Ltd |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Equity method investment, ownership interest, percent |  | 50.00% |  | 50.00% |
Proceeds from sale of equity method investments |  | $ 535,000 |  |  |
Cost of services provided | FSS United States |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  |  |  | $ 19,000 |
Cost of services provided | FSS United States | Right Of Use Assets |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  |  |  | 8,600 |
Cost of services provided | FSS United States | Leasehold Improvements |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  |  |  | 10,400 |
Captive |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Cash and cash equivalents | 15,700 |  | 15,700 |  | 32,800
Investment at cost | $ 114,300 |  | $ 114,300 |  | $ 110,700
Foreign Countries Outside North America |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Number of foreign countries in which entity operates | country | 14 |  | 14 |  |
ARGENTINA |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Foreign currency transaction loss | $ 400 | $ 2,800 | $ 5,200 | $ 6,700 |

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