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Pension and Other Postretirement Benefit Plans - Schedule of Components of Net Periodic Pension Cost (Details) - USD ($)
$ in Thousands
 12 Months Ended
Sep. 30, 2022
Oct. 01, 2021
Oct. 02, 2020
Defined Benefit Plan Disclosure [Line Items]      
Defined Benefit Plan, Net Periodic Benefit Cost (Credit) Excluding Service Cost, Statement of Income or Comprehensive Income [Extensible Enumeration] Nonoperating Income (Expense) Nonoperating Income (Expense) Nonoperating Income (Expense)
Pension Plan | U.S. Plans      
Defined Benefit Plan Disclosure [Line Items]      
Service cost $ 236 $ 456 $ 409
Interest cost 10,350 10,221 12,673
Expected return on plan assets (16,933) (15,932) (17,670)
Actuarial loss 2,861 4,249 3,518
Prior service cost 430 431 323
Net pension cost, before special items (3,056) (575) (747)
Curtailment expense/Settlement loss (206) (64) 3,436
Total net periodic pension (income) cost recognized (3,262) (639) 2,689
Pension Plan | Non-U.S. Plans      
Defined Benefit Plan Disclosure [Line Items]      
Service cost 6,480 6,568 5,710
Interest cost 42,328 38,907 39,469
Expected return on plan assets (71,875) (90,346) (93,407)
Actuarial loss 7,147 10,834 7,578
Prior service cost 1,421 1,519 1,405
Net pension cost, before special items (14,499) (32,518) (39,245)
Curtailment expense/Settlement loss 329 2,847 1,341
Total net periodic pension (income) cost recognized $ (14,170) $ (29,671) $ (37,904)