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Basis of Presentation and Summary of Significant Accounting Policies - Narrative (Details) | 3 Months Ended | 6 Months Ended | 12 Months Ended
--- | --- | --- | ---
Mar. 29, 2024 USD ($) country | Mar. 31, 2023 USD ($) | Mar. 29, 2024 USD ($) segment country | Mar. 31, 2023 USD ($) | 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 |  |  | $ 5,100,000 |  |
Foreign currency translation adjustments, spin-off |  |  | 26,300,000 |  |
Foreign currency transaction loss | $ 900,000 | $ 2,800,000 | 4,800,000 | $ 3,900,000 |
Cash and cash equivalents | 356,605,000 | 292,199,000 | 356,605,000 | 292,199,000 | $ 1,927,088,000
Impairment charges |  |  | 0 | 27,781,000 |
Equity method investment, aggregate cost | 71,600,000 |  | 71,600,000 |  | 73,500,000
Equity securities without readily determinable fair value, amount | 83,600,000 |  | 83,600,000 |  | 83,600,000
Supplier finance program, obligation | 2,200,000 |  | 2,200,000 |  | 2,800,000
Cost of services provided | FSS - United States |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  | 700,000 |  | 19,000,000 |
Cost of services provided | FSS - United States | Right Of Use Assets |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  | 700,000 |  | 8,600,000 |
Cost of services provided | FSS - United States | Leasehold Improvements |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Impairment charges |  | $ 0 |  | $ 10,400,000 |
Deferred Income Taxes and Other Noncurrent Liabilities | CARES Act |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Payment of deferred social security taxes |  |  |  |  | 47,600,000
Captive |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Cash and cash equivalents | 13,200,000 |  | 13,200,000 |  | 32,800,000
Captive | Prepaid Expenses and Other Current Assets |  |  |  |  |
Basis of Presentation and Summary of Significant Accounting Policies [Line Items] |  |  |  |  |
Investment at cost | $ 112,800,000 |  | $ 112,800,000 |  | $ 110,700,000
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 |  |

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