Revenue from Contracts with Customers - Schedule of Disaggregation of Revenue (Details) - USD ($) $ in Thousands	3 Months Ended
	Dec. 31, 2022	Jan. 01, 2022
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	$ 1,120,939	$ 841,881
Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,093,925	817,456
Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	27,014	24,425
Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	472,082	363,827
Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	487,867	344,465
Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	133,976	109,164
AMER
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	389,662	277,346
AMER | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	386,430	274,957
AMER | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	3,232	2,389
AMER | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	103,027	83,245
AMER | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	215,381	135,962
AMER | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	68,022	55,750
APAC
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	641,904	491,672
APAC | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	619,528	470,255
APAC | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	22,376	21,417
APAC | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	350,584	265,275
APAC | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	223,290	169,237
APAC | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	45,654	35,743
EMEA
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	89,373	72,863
EMEA | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	87,967	72,244
EMEA | Elimination of inter-segment sales
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	1,406	619
EMEA | Industrial | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	18,471	15,307
EMEA | Healthcare/Life Sciences | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	49,196	39,266
EMEA | Aerospace/Defense | Operating Segments
Disaggregation of Revenue [Line Items]
Revenue from Contract with Customer	$ 20,300	$ 17,671