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Segment Information - Schedule of Total Revenues, Segment Operating Profit and Total Asset for Reporting Segment (Details) - USD ($)
$ in Thousands
 3 Months Ended
Dec. 30, 2022
Dec. 31, 2021
Segment Reporting Information [Line Items]    
Revenues $ 3,798,668 $ 3,380,625
Total Segment Operating Profit 237,805 177,333
Restructuring, Transaction and Other Charges (40,342) (83,566)
Total Other Income (Expense), net (40,324) (8,243)
Earnings from Continuing Operations Before Taxes 197,481 169,090
Amortization of intangible assets 49,773  
Real estate impairment charges 27,100 72,300
Gain related to cost-method Investments   6,900
Operating Segments    
Segment Reporting Information [Line Items]    
Total Segment Operating Profit 371,833 366,259
Corporate    
Segment Reporting Information [Line Items]    
Other Corporate Expenses (93,686) (105,360)
Corporate | Other Expense    
Segment Reporting Information [Line Items]    
Amortization of intangible assets 49,800 46,900
One-time benefit program changes 15,000  
Changes in employee benefit programs 41,000  
Company technology platforms and other personnel and corporate overhead cost increases 26,000  
Critical Mission Solutions | Operating Segments    
Segment Reporting Information [Line Items]    
Revenues 1,075,175 976,777
Total Segment Operating Profit 82,220 91,239
People & Places Solutions | Operating Segments    
Segment Reporting Information [Line Items]    
Revenues 2,226,985 1,920,997
Total Segment Operating Profit 226,619 188,841
Divergent Solutions | Operating Segments    
Segment Reporting Information [Line Items]    
Revenues 214,465 192,877
Total Segment Operating Profit 11,967 23,108
PA Consulting | Operating Segments    
Segment Reporting Information [Line Items]    
Revenues 282,043 289,974
Total Segment Operating Profit $ 51,027 $ 63,071