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Income Taxes - Narrative (Details) - USD ($) $ in Thousands | 12 Months Ended
--- | ---
Sep. 29, 2023 | Sep. 30, 2022 | Oct. 01, 2021
Tax Credit Carryforward [Line Items] |  |  |
Current (benefit) provision for income taxes |  |  | $ 16,700
Tax benefit to the deferred (benefit) provision for income taxes related to a corresponding decrease in deferred tax liabilities |  |  | 13,800
Net tax expense to the (benefit) provision for income taxes related to unrecognized tax benefits |  |  | 2,900
Current income tax assets | $ 10,198 | $ 10,842 |
Accrued taxes | 25,000 | 2,600 |
Proceeds from income tax refunds |  |  | 93,600
Net tax expense to provision (benefit) for income taxes | 76,700 | (4,200) |
Gains and Losses from restructuring of certain foreign subsidiaries | 21,700 |  |
Income tax expense (benefit) | 177,614 | 61,461 | (40,633)
Net operating loss carried back to Pre-TCJA years |  |  | 50,300
Valuation allowances | 78,194 | 83,827 | 97,472
Decrease in income taxes receivable |  |  | 1,800
Foreign tax credit carryforwards | 74,400 |  |
Tax credit carry forward, general business | 800 |  |
Deferred tax payable | 583,832 | 470,606 |
Operating loss carryforwards | 85,500 |  |
Undistributed foreign earnings | 455,900 | 347,200 |
Tax liability on undistributed foreign earnings | 27,300 | 20,400 |
Gross unrecognized tax benefits | 70,313 | 80,220 | 65,414
Unrecognized tax benefits that would impact the effective tax rate | 39,900 |  |
Adjustment in deferred tax liability | 30,400 |  |
Accrued for interest and penalties | 11,400 | 9,700 |
Income tax penalties and interest expense | 1,700 | 3,100 | 2,000
AIM Services Co., Ltd |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Gains and Losses from restructuring of certain foreign subsidiaries | 98,400 |  |
Foreign Tax Credit Carryforward |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Tax credit carryforward, amount | 9,600 |  |
Valuation Allowance, Operating Loss Carryforwards |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Valuation allowances | 47,100 |  |
Deferred Income Taxes and Other Noncurrent Liabilities |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Deferred tax payable | 610,500 | 501,400 |
Other assets |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Deferred tax assets | 26,700 | 30,800 |
Foreign Tax Authority | Foreign Tax Credit Carryforward |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Tax credit carryforward, Interest | 31,100 |  |
Foreign Tax Authority | Canada Revenue Agency |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Tax adjustments, settlements, and unusual provisions | 4,000 |  |
State and Local Jurisdiction |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Valuation allowances | 10,100 |  |
CARES Act |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Income tax expense (benefit) |  |  | 12,000
Valuation allowances |  |  | 36,500
Income taxes receivable |  |  | 3,700
Foreign tax credit carryforwards |  |  | 71,300
Tax credit carry forward, general business |  |  | 11,000
FSS International |  |  |
Tax Credit Carryforward [Line Items] |  |  |
Deferred tax asset, increase (decrease), amount | $ 3,800 | $ 8,500 | $ (22,000)

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