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Revenue from Contracts with Customers - Schedule of Disaggregation of Revenue (Details) - USD ($)
$ in Thousands
3 Months Ended
Jan. 01, 2022
Jan. 02, 2021
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer $ 841,881 $ 857,592
Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 817,456 830,355
Elimination of inter-segment sales    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 24,425 27,237
Industrial | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 363,827 378,042
Healthcare/Life Sciences | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 344,465 319,313
Aerospace/Defense | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 109,164 133,000
AMER    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 277,346 327,567
AMER | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 274,957 325,445
AMER | Elimination of inter-segment sales    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 2,389 2,122
AMER | Industrial | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 83,245 122,026
AMER | Healthcare/Life Sciences | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 135,962 126,439
AMER | Aerospace/Defense | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 55,750 76,980
APAC    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 491,672 451,302
APAC | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 470,255 426,553
APAC | Elimination of inter-segment sales    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 21,417 24,749
APAC | Industrial | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 265,275 238,248
APAC | Healthcare/Life Sciences | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 169,237 154,046
APAC | Aerospace/Defense | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 35,743 34,259
EMEA    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 72,863 78,723
EMEA | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 72,244 78,357
EMEA | Elimination of inter-segment sales    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 619 366
EMEA | Industrial | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 15,307 17,768
EMEA | Healthcare/Life Sciences | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer 39,266 38,828
EMEA | Aerospace/Defense | Operating Segments    
Disaggregation of Revenue [Line Items]    
Revenue from Contract with Customer $ 17,671 $ 21,761