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Debt - Credit Agreement - Additional Information (Details) - USD ($) | 3 Months Ended | 12 Months Ended |
--- | --- | --- | ---
Jun. 27, 2020 | Mar. 28, 2020 | Dec. 28, 2019 | Sep. 30, 2022 | Sep. 30, 2021 | Sep. 30, 2020 | Feb. 13, 2020
Debt Instrument [Line Items] |  |  |  |  |  |  |
Credit facility amount |  |  |  |  |  |  | $ 1,000,000,000
Voting interest in domestic subsidiaries pledged against credit facility |  |  |  | 100.00% |  |  |
Voting interest in foreign subsidiaries pledged against credit facility |  |  |  | 65.00% |  |  |
Leverage ratio, actual |  |  |  | 1.79 |  |  |
Senior debt leverage ratio, actual |  |  |  | 0.49 |  |  |
Fixed charge coverage ratio, actual |  |  |  | 14.21 |  |  |
Financing costs |  |  |  | $ 0 | $ 0 | $ 17,107,000 |
Interest expense |  |  |  | 54,300,000 | 50,500,000 | 76,400,000 |
Periodic interest payment |  |  |  | $ 48,500,000 | $ 45,200,000 | $ 60,600,000 |
Amount paid in penalties for the early redemption of the 2024 notes | $ 15,000,000.0 |  |  |  |  |  |
Interest rate during period |  |  |  | 3.40% | 3.30% | 4.30% |
Line of Credit |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Line of credit facility, maximum borrowing capacity expansion amount |  |  |  |  |  |  | $ 500,000,000
Unused commitments under credit facility |  |  |  | $ 641,000,000.0 |  |  |
Credit facility maturity date |  |  |  | Feb. 13, 2025 |  |  |
Basis spread on Federal Reserve Bank of New York (FRBNY) rate |  |  |  | 0.50% |  |  |
Basis spread on adjusted LIBOR |  |  |  | 1.00% |  |  |
Investment limit in foreign subsidiaries |  |  |  | $ 100,000,000 |  |  |
Cash investment limit for acquisition of business |  |  |  | $ 200,000,000 |  |  |
Total leverage ratio |  |  |  | 4.50 |  |  |
Senior secured leverage ratio |  |  |  | 3.00 |  |  |
Minimum fixed charge coverage ratio allowed under debt covenant |  |  |  | 3.00 |  |  |
Financing costs |  | $ 2,000,000.0 | $ 1,000,000.0 |  |  |  |
Line of Credit | Minimum |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Variable interest rate, length of time between updates |  |  |  | 30 days |  |  |
Credit facility commitment fees percentage |  |  |  | 0.175% |  |  |
Line of Credit | Minimum | London Interbank Offered Rate (LIBOR) |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Basis spread on variable rate |  |  |  | 1.25% |  |  |
Line of Credit | Minimum | Base Rate |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Basis spread on variable rate |  |  |  | 0.25% |  |  |
Line of Credit | Maximum |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Variable interest rate, length of time between updates |  |  |  | 180 days |  |  |
Credit facility commitment fees percentage |  |  |  | 0.30% |  |  |
Line of Credit | Maximum | London Interbank Offered Rate (LIBOR) |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Basis spread on variable rate |  |  |  | 1.75% |  |  |
Line of Credit | Maximum | Base Rate |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Basis spread on variable rate |  |  |  | 0.75% |  |  |
Secured Debt | Revolving Loan, Reset Period One |  |  |  |  |  |  |
Debt Instrument [Line Items] |  |  |  |  |  |  |
Interest rate at period end |  |  |  | 4.14% |  |  |

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