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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 3 Months Ended | 6 Months Ended
--- | --- | ---
Mar. 31, 2019 | Mar. 31, 2018 | Mar. 31, 2019 | Mar. 31, 2018
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | $ 736,520 | $ 612,787 | $ 1,401,139 | $ 1,235,935
United States of America |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 580,473 |  | 1,091,673 |
United Kingdom |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 78,334 |  | 151,752 |
Australia |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 50,997 |  | 104,370 |
Rest of world |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 26,716 |  | 53,344 |
Total U.S. state government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 287,728 |  | 578,342 |
New York State government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 89,858 |  | 181,570 |
Other U.S. state government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 197,870 |  | 396,772 |
United States Federal Government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 270,623 |  | 468,901 |
International government agencies |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 146,292 |  | 289,073 |
Other, including local municipalities and commercial customers |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 31,877 |  | 64,823 |
Performance-based |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 261,592 |  | 574,479 |
Cost-plus |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 298,133 |  | 473,431 |
Fixed price |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 139,871 |  | 287,022 |
Time and materials |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 36,924 |  | 66,207 |
U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 290,737 |  | 584,950 |
U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 289,736 |  | 506,723 |
Outside the U.S. |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 156,047 |  | 309,466 |
Program administration | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 219,732 |  | 438,705 |
Program administration | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 209,996 |  | 350,117 |
Program administration | Outside the U.S. |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 15,922 |  | 31,242 |
Assessments and appeals | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 33,331 |  | 70,552 |
Assessments and appeals | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 41,747 |  | 79,730 |
Assessments and appeals | Outside the U.S. |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 67,771 |  | 130,081 |
Workforce and children services | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 23,898 |  | 47,801 |
Workforce and children services | Outside the U.S. |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 69,759 |  | 143,037 |
Other | U.S. Health & Human Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 13,776 |  | 27,892 |
Other | Outside the U.S. |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | 2,595 |  | 5,106 |
Technology solutions | U.S. Federal Services |  |  |  |
Disaggregation of Revenue [Line Items] |  |  |  |
Revenue | $ 37,993 |  | $ 76,876 |

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