| Disaggregation of Revenue | By operating segment and service 
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
|  |  | Three Months Ended June 30, |  |  |  | Nine Months Ended June 30, |  |  |  
| (dollars in thousands) |  | 2020 |  | 2019 |  | 2020 |  | 2019 |  
| Program administration |  | $ | 251,616 |  |  | $ | 212,638 |  |  | $ | 724,960 |  |  | $ | 651,343 |  |  
| Assessments and appeals |  | 40,875 |  |  | 35,657 |  |  | 104,621 |  |  | 106,209 |  |  
| Workforce and children services |  | 32,531 |  |  | 29,146 |  |  | 90,651 |  |  | 76,947 |  |  
| Other |  | 11,928 |  |  | 13,691 |  |  | 37,697 |  |  | 41,583 |  |  
| Total U.S. Health and Human Services |  | $ | 336,950 |  |  | $ | 291,132 |  |  | $ | 957,929 |  |  | $ | 876,082 |  |  
|  |  |  |  |  |  |  |  |  |  
| Program administration |  | $ | 362,973 |  |  | $ | 204,622 |  |  | $ | 949,071 |  |  | $ | 554,739 |  |  
| Technology solutions |  | 42,101 |  |  | 39,994 |  |  | 130,172 |  |  | 116,870 |  |  
| Assessments and appeals |  | 45,069 |  |  | 47,679 |  |  | 130,862 |  |  | 127,409 |  |  
| Total U.S. Federal Services |  | $ | 450,143 |  |  | $ | 292,295 |  |  | $ | 1,210,105 |  |  | $ | 799,018 |  |  
|  |  |  |  |  |  |  |  |  |  
| Workforce and children services |  | $ | 55,046 |  |  | $ | 65,819 |  |  | $ | 146,968 |  |  | $ | 208,856 |  |  
| Assessments and appeals |  | 42,468 |  |  | 62,152 |  |  | 167,397 |  |  | 192,233 |  |  
| Program administration |  | 15,544 |  |  | 16,767 |  |  | 49,583 |  |  | 48,009 |  |  
| Other |  | 1,186 |  |  | 2,545 |  |  | 5,719 |  |  | 7,651 |  |  
| Total Outside the U.S. |  | $ | 114,244 |  |  | $ | 147,283 |  |  | $ | 369,667 |  |  | $ | 456,749 |  |  
|  |  |  |  |  |  |  |  |  |  
| Total revenue |  | $ | 901,337 |  |  | $ | 730,710 |  |  | $ | 2,537,701 |  |  | $ | 2,131,849 |  | 
 By contract type 
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
|  |  | Three Months Ended June 30, |  |  |  | Nine Months Ended June 30, |  |  |  
| (dollars in thousands) |  | 2020 |  | 2019 |  | 2020 |  | 2019 |  
| Performance-based |  | $ | 295,650 |  |  | $ | 260,052 |  |  | $ | 864,077 |  |  | $ | 834,531 |  |  
| Cost-plus |  | 422,641 |  |  | 282,795 |  |  | 1,184,425 |  |  | 756,227 |  |  
| Fixed price |  | 132,535 |  |  | 142,940 |  |  | 352,255 |  |  | 429,962 |  |  
| Time and materials |  | 50,511 |  |  | 44,923 |  |  | 136,944 |  |  | 111,129 |  |  
| Total revenue |  | $ | 901,337 |  |  | $ | 730,710 |  |  | $ | 2,537,701 |  |  | $ | 2,131,849 |  | By customer type 
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
|  |  | Three Months Ended June 30, |  |  |  | Nine Months Ended June 30, |  |  |  
| (dollars in thousands) |  | 2020 |  | 2019 |  | 2020 |  | 2019 |  
| New York State government agencies |  | $ | 79,140 |  |  | $ | 90,295 |  |  | $ | 276,585 |  |  | $ | 271,865 |  |  
| Other U.S. state government agencies |  | 265,608 |  |  | 204,272 |  |  | 692,689 |  |  | 601,044 |  |  
| Total U.S. state government agencies |  | 344,748 |  |  | 294,567 |  |  | 969,274 |  |  | 872,909 |  |  
|  |  |  |  |  |  |  |  |  |  
| United States Federal Government agencies |  | 429,031 |  |  | 276,294 |  |  | 1,155,773 |  |  | 745,195 |  |  
| International government agencies |  | 107,353 |  |  | 136,848 |  |  | 345,629 |  |  | 425,921 |  |  
| Other, including local municipalities and commercial customers |  | 20,205 |  |  | 23,001 |  |  | 67,025 |  |  | 87,824 |  |  
| Total revenue |  | $ | 901,337 |  |  | $ | 730,710 |  |  | $ | 2,537,701 |  |  | $ | 2,131,849 |  | 
 By geography 
|  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  |  
|  |  | Three Months Ended June 30, |  |  |  | Nine Months Ended June 30, |  |  |  
| (dollars in thousands) |  | 2020 |  | 2019 |  | 2020 |  | 2019 |  
| United States of America |  | $ | 787,092 |  |  | $ | 583,428 |  |  | $ | 2,168,033 |  |  | $ | 1,675,101 |  |  
| United Kingdom |  | 53,364 |  |  | 72,265 |  |  | 190,088 |  |  | 224,017 |  |  
| Australia |  | 38,415 |  |  | 48,744 |  |  | 100,390 |  |  | 153,114 |  |  
| Rest of world |  | 22,466 |  |  | 26,273 |  |  | 79,190 |  |  | 79,617 |  |  
| Total revenue |  | $ | 901,337 |  |  | $ | 730,710 |  |  | $ | 2,537,701 |  |  | $ | 2,131,849 |  |  |