Income Taxes - Narrative (Details) - USD ($) $ in Thousands	12 Months Ended
Sep. 27, 2024	Sep. 29, 2023	Sep. 30, 2022
Tax Credit Carryforward [Line Items]
Current income tax assets	$ 3,829	$ 10,198
Accrued taxes	19,300	24,500
Net tax expense to provision (benefit) for income taxes		76,700	$ (3,800)
Gains and Losses from restructuring of certain foreign subsidiaries		21,700
Deferred tax payable	355,387	384,293
Operating loss carryforwards	72,100
Valuation allowances	80,552	78,194	83,827
Foreign tax credit carryforwards	61,700
Tax credit carry forward, general business	3,400
Undistributed foreign earnings	446,700	364,400
Tax liability on undistributed foreign earnings	26,800	22,700
Gross unrecognized tax benefits	70,188	69,128	80,220
Unrecognized tax benefits that would impact the effective tax rate	41,900
Adjustment in deferred tax liability	28,300
Accrued for interest and penalties	14,100	11,400
Income tax penalties and interest expense	2,800	1,700	3,100
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	48,200
Deferred Income Taxes and Other Noncurrent Liabilities
Tax Credit Carryforward [Line Items]
Deferred tax payable	375,400	410,900
Deferred Income Taxes And OtherTax Liabilities, Noncurrent
Tax Credit Carryforward [Line Items]
Deferred tax assets, net	20,000	26,600
Foreign Tax Jurisdiction \| Foreign Tax Credit Carryforward
Tax Credit Carryforward [Line Items]
Tax credit carryforward, Interest	32,300
State and Local Jurisdiction
Tax Credit Carryforward [Line Items]
Valuation allowances	34,100
AIM Services Co., Ltd
Tax Credit Carryforward [Line Items]
Gains and Losses from restructuring of certain foreign subsidiaries		98,400
FSS International
Tax Credit Carryforward [Line Items]
Deferred tax asset, increase (decrease), amount	$ 3,800	$ 3,800	$ 8,500

Amount after allocation of valuation allowances of deferred tax asset attributable to deductible temporary differences and carryforwards.

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