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Income Taxes - Narrative (Details)
$ in Thousands
12 Months Ended
Oct. 03, 2025
USD ($)
Sep. 27, 2024
USD ($)
Sep. 29, 2023
USD ($)
Dec. 31, 2021
country
Tax Credit Carryforward [Line Items]        
Current income tax assets $ 26,803 $ 3,829    
Accrued taxes 19,500 19,300    
Net tax expense to provision (benefit) for income taxes     $ 76,700  
Gains and losses from restructuring of certain foreign subsidiaries     21,700  
Deferred tax payable 378,280 355,387    
Operating loss carryforwards 64,700      
Valuation allowances 62,276 80,552 78,194  
Foreign tax credit carryforwards 57,200      
Tax credit carry forward, general business 2,800      
Undistributed foreign earnings 574,900 446,700    
Tax liability on undistributed foreign earnings 33,800 26,800    
Gross unrecognized tax benefits 88,605 70,188 69,128  
Unrecognized tax benefits that would impact the effective tax rate 59,700      
Adjustment in deferred tax liability 28,900      
Accrued for interest and penalties 18,400 14,100    
Income tax penalties and interest expense 4,300 2,800 1,700  
Number of countries agreed to enact pillar two legislation | country       140
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 27,000      
Deferred Income Taxes and Other Noncurrent Liabilities        
Tax Credit Carryforward [Line Items]        
Deferred tax payable 410,900 375,400    
Deferred Income Taxes And OtherTax Liabilities, Noncurrent        
Tax Credit Carryforward [Line Items]        
Deferred tax assets, net 32,600 20,000    
State and Local Jurisdiction        
Tax Credit Carryforward [Line Items]        
Valuation allowances 39,400      
Foreign Tax Jurisdiction | Foreign Tax Credit Carryforward        
Tax Credit Carryforward [Line Items]        
Tax credit carryforward, interest 35,200      
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 $ 24,800 $ 3,800 $ 3,800