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Income Taxes - Narrative (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2022
Oct. 01, 2021
Oct. 02, 2020
Sep. 27, 2019
Income Tax Contingency [Line Items]        
Tax Rate Change $ 3,210 $ 25,588 $ (6,811)  
Valuation allowance 113,483 188,662    
Change in deferred tax asset valuation (75,200)      
Change in deferred tax assets valuation allowance, amount (59,121) 38,928 0  
Change in deferred tax assets valuation allowance due to other various changes (16,100)      
Net operating losses 132,999 197,929    
Foreign currency valuation allowance 55,400      
Undistributed earnings of foreign subsidiaries 168,000      
Amount of unrecognized deferred tax liability not recognized due to undistributed earnings of foreign subsidiaries 13,100      
Gross unrecognized tax benefits 88,893 113,633 102,484 $ 104,355
Unrecognized tax benefits 88,893 113,633 102,484 $ 104,355
Unrecognized tax benefits that would impact effective tax rate 73,500      
Accrued interest and penalties 43,500 41,600    
Decrease in unrecognized tax benefits 2,200      
Other items – net 5,677 (896) $ (788)  
Affiliated Entity        
Income Tax Contingency [Line Items]        
Undistributed earnings of foreign subsidiaries 101,700      
Amount of unrecognized deferred tax liability not recognized due to undistributed earnings of foreign subsidiaries 25,000      
Capital Loss Carryforward        
Income Tax Contingency [Line Items]        
Change in deferred tax assets valuation allowance, amount 26,000      
Accounting Standards Update 2013-11        
Income Tax Contingency [Line Items]        
Gross unrecognized tax benefits 81,900 91,900    
Unrecognized tax benefits 81,900 91,900    
Accounting Standards Update 2013-11 | Cumulative Effect, Period of Adoption, Adjustment        
Income Tax Contingency [Line Items]        
Gross unrecognized tax benefits 7,000 21,700    
Unrecognized tax benefits 7,000 21,700    
United States Federal Tax Authority        
Income Tax Contingency [Line Items]        
Change in deferred tax assets valuation allowance, amount 33,100      
Foreign Country        
Income Tax Contingency [Line Items]        
Loss carry forwards of foreign subsidiaries 491,300 760,400    
Foreign Country | Her Majesty's Revenue and Customs (HMRC)        
Income Tax Contingency [Line Items]        
Tax Rate Change 3,200 $ 25,600    
Expiring Between 2022 and 2031 | Foreign Country        
Income Tax Contingency [Line Items]        
Loss carry forwards of foreign subsidiaries $ 83,700