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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 12 Months Ended
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Sep. 30, 2024 | Sep. 30, 2023 | Sep. 30, 2022
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 5,306,197 | $ 4,904,728 | $ 4,631,018
New York state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 647,349 | $ 525,051 | $ 389,004
New York state government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 12.20% | 10.70% | 8.40%
Other U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,255,181 | $ 1,275,763 | $ 1,216,453
Other U.S. state government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 23.70% | 26.00% | 26.30%
Total U.S. state government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,902,530 | $ 1,800,814 | $ 1,605,457
United States federal government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,674,014 | $ 2,344,863 | $ 2,189,303
United States federal government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 50.40% | 47.80% | 47.30%
International government agencies |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 642,222 | $ 663,044 | $ 722,192
International government agencies | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 12.10% | 13.50% | 15.60%
Other, including local municipalities and commercial customers |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 87,431 | $ 96,007 | $ 114,066
Other, including local municipalities and commercial customers | Revenue Benchmark | Customer Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 1.60% | 2.00% | 2.50%
Performance-based |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,939,536 | $ 2,425,597 | $ 2,091,608
Performance-based | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 55.40% | 49.50% | 45.20%
Cost-plus |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,247,202 | $ 1,238,574 | $ 1,248,759
Cost-plus | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 23.50% | 25.30% | 27.00%
Fixed price |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 686,555 | $ 717,167 | $ 627,402
Fixed price | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 12.90% | 14.60% | 13.50%
Time and materials |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 432,904 | $ 523,390 | $ 663,249
Time and materials | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 8.20% | 10.70% | 14.30%
Program Operations |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 2,570,494 | $ 2,500,678 | $ 2,502,620
Program Operations | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 48.40% | 51.00% | 54.00%
Clinical Services |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 1,891,292 | $ 1,486,040 | $ 1,176,081
Clinical Services | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 35.60% | 30.30% | 25.40%
Employment & Other |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 469,304 | $ 520,981 | $ 551,755
Employment & Other | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 8.80% | 10.60% | 11.90%
Technology Solutions |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue | $ 375,107 | $ 397,029 | $ 400,562
Technology Solutions | Revenue Benchmark | Contract Concentration Risk |  |  |
Disaggregation of Revenue [Line Items] |  |  |
Revenue in % | 7.10% | 8.10% | 8.60%

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