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Revenue Recognition - Disaggregation of Revenue (Details) - USD ($) $ in Thousands | 3 Months Ended
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Dec. 31, 2021 | Dec. 31, 2020
Disaggregation of Revenue [Line Items] |  |
Revenue | $ 1,150,876 | $ 945,554
United States |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 968,288 | 790,179
United Kingdom |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 85,807 | 64,786
Australia |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 52,814 | 55,932
Rest of world |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 43,967 | 34,657
U.S. state government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 371,547 | 388,114
United States Federal Government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 564,094 | 385,573
International government agencies |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 171,375 | 147,342
Other, including local municipalities and commercial customers |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 43,860 | 24,525
Performance-based |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 490,956 | 293,960
Cost-plus |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 340,081 | 384,483
Fixed price |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | 151,505 | 120,777
Time and materials |  |
Disaggregation of Revenue [Line Items] |  |
Revenue | $ 168,334 | $ 146,334

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- Definition Amount, excluding tax collected from customer, of revenue from satisfaction of performance obligation by transferring promised good or service to customer. Tax collected from customer is tax assessed by governmental authority that is both imposed on and concurrent with specific revenue-producing transaction, including, but not limited to, sales, use, value added and excise. + References Reference 1: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 30 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e8906-108599 Reference 2: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 40 -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e9031-108599 Reference 3: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 41 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e9038-108599 Reference 4: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 32 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e8933-108599 Reference 5: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 32 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e8933-108599 Reference 6: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 606 -SubTopic 10 -Section 50 -Paragraph 4 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123351226&loc=SL49130543-203045 Reference 7: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 22 -Subparagraph (b) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e8736-108599 Reference 8: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 22 -Subparagraph (a) -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e8736-108599 Reference 9: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 280 -SubTopic 10 -Section 50 -Paragraph 42 -URI http://asc.fasb.org/extlink&oid=123359005&loc=d3e9054-108599 Reference 10: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 606 -SubTopic 10 -Section 50 -Paragraph 5 -URI http://asc.fasb.org/extlink&oid=123351226&loc=SL49130545-203045 Reference 11: http://www.xbrl.org/2003/role/disclosureRef -Publisher FASB -Name Accounting Standards Codification -Topic 924 -SubTopic 10 -Section S99 -Paragraph 1 -Subparagraph (SAB Topic 11.L) -URI http://asc.fasb.org/extlink&oid=6472922&loc=d3e499488-122856 + Details
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