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Reportable Segments - Schedule of Reportable Segments Information (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Apr. 02, 2022
Apr. 03, 2021
Apr. 02, 2022
Apr. 03, 2021
Oct. 02, 2021
Net sales $ 888,723 $ 880,885 $ 1,706,179 $ 1,711,240  
Operating Income (Loss) 35,837 50,687 66,310 97,553  
Total assets 2,990,048   2,990,048   $ 2,461,893
Other income (expense):          
Interest Expense (3,345) (3,818) (6,391) (7,904)  
Investment Income, Interest 262 390 533 764  
Other Nonoperating Income (Expense) (1,446) (825) (2,369) (2,343)  
Income (Loss) from Continuing Operations before Income Taxes, Noncontrolling Interest 31,308 46,434 58,083 88,070  
Elimination of inter-segment sales          
Net sales (30,069) (26,006) (54,494) (53,243)  
Corporate and other costs          
Operating Income (Loss) (33,282) (32,010) (66,243) (62,180)  
Corporate and eliminations          
Total assets 105,857   105,857   114,262
AMER | Operating Segments          
Net sales 311,205 364,697 588,551 692,264  
Operating Income (Loss) 7,769 26,203 9,559 42,685  
Total assets 962,320   962,320   789,385
APAC | Operating Segments          
Net sales 533,885 458,872 1,025,557 910,174  
Operating Income (Loss) 60,860 58,112 121,548 119,654  
Total assets 1,626,518   1,626,518   1,283,124
EMEA | Operating Segments          
Net sales 73,702 83,322 146,565 162,045  
Operating Income (Loss) 490 $ (1,618) 1,446 $ (2,606)  
Total assets $ 295,353   $ 295,353   $ 275,122