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Pension and Other Postretirement Benefit Plans - Schedule of Pension Plans Recognized in Accumulated Other Comprehensive Loss (Details) - USD ($)
$ in Thousands
12 Months Ended
Sep. 30, 2022
Oct. 01, 2021
Oct. 02, 2020
Reclassification adjustments:      
Total $ (87,166) $ (104,165) $ 61,977
Pension Plan | U.S. Plans      
Arising during the period:      
Net actuarial loss (gain) 578 (25,109) (900)
Prior service cost 0 0 1,589
Total 578 (25,109) 689
Reclassification adjustments:      
Net actuarial losses (2,157) (3,204) (2,653)
Prior service (benefit) (324) (325) (244)
Total (2,481) (3,529) (2,897)
Total (1,903) (28,638) (2,208)
Pension Plan | Non-U.S. Plans      
Arising during the period:      
Net actuarial loss (gain) (78,705) (65,547) 71,676
Prior service cost 0 0 0
Total (78,705) (65,547) 71,676
Reclassification adjustments:      
Net actuarial losses (5,492) (8,761) (6,322)
Prior service (benefit) (1,066) (1,219) (1,169)
Total (6,558) (9,980) (7,491)
Total $ (85,263) $ (75,527) $ 64,185