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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 3 Months Ended
--- | ---
Dec. 31, 2020 | Dec. 31, 2019
Disaggregation of Revenue [Line Items] |  |
Revenue | $ 945,554 | $ 818,229
United States |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 790,179 | 678,852
United Kingdom |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 64,786 | 73,002
Australia |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 55,932 | 37,435
Rest of world |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 34,657 | 28,940
Total U.S. state government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 388,114 | 307,109
New York State government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 75,356 | 97,223
Other U.S. state government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 312,758 | 209,886
United States Federal Government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 385,573 | 351,833
International government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 147,342 | 130,816
Other, including local municipalities and commercial customers |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 24,525 | 28,471
Performance-based |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 293,960 | 292,758
Cost-plus |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 384,483 | 362,811
Fixed price |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 120,777 | 119,216
Time and materials |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 146,334 | 43,444
U.S. Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 384,934 | 312,281
U.S. Federal Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 405,245 | 366,571
Outside the U.S. |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 155,375 | 139,377
Program administration | U.S. Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 293,844 | 236,907
Program administration | U.S. Federal Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 327,790 | 281,688
Program administration | Outside the U.S. |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 23,056 | 17,094
Technology solutions | U.S. Federal Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 34,664 | 43,606
Assessments and appeals | U.S. Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 32,615 | 33,831
Assessments and appeals | U.S. Federal Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 42,791 | 41,277
Assessments and appeals | Outside the U.S. |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 53,123 | 62,643
Workforce and children services | U.S. Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 47,821 | 29,386
Workforce and children services | Outside the U.S. |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 77,462 | 57,239
Other | U.S. Services |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 10,654 | 12,157
Other | Outside the U.S. |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | $ 1,734 | $ 2,401

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