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Restatement of previously reported unaudited interim consolidated financial statements - Schedule of Cashflows (Details) - USD ($)
$ in Thousands
 3 Months Ended 6 Months Ended
Mar. 31, 2023
Mar. 31, 2022
Mar. 31, 2023
Mar. 31, 2022
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Net income $ 5,169 $ 435 $ 9,899 $ 3,559
Adjustments to reconcile net income to net cash provided by operating activities:        
Stock-based compensation expense     5,146 6,429
Amortization of intangible assets 4,500 2,400 9,007 4,525
Depreciation and amortization     767 555
Amortization of investment premiums & other     (26) 1,109
Accretion and amortization on debt securities     3,700 3,453
Net changes in estimated fair value of acquisition-related contingent consideration     150 (1,370)
Deferred taxes     (6,827) (763)
Changes in assets and liabilities, net of acquisitions:        
Accounts receivable     (7,379) (6,095)
Contract assets     (4,969) 345
Other assets     (753) 450
Accounts payable     367 3,769
Accrued payroll and related taxes     (2,724) (4,693)
Deferred revenue     (2,429) (2,215)
Other liabilities       628
Net cash provided by operating activities     11,561 9,686
Investing activities:        
Purchases of investments     0 (47,818)
Sales and maturities of investments     38,100 173,316
Acquisitions, net of cash acquired     0 (126,607)
Purchases of property and equipment     (372) (634)
Net cash provided by (used in) investing activities     37,728 (1,743)
Financing activities:        
Proceeds from the issuance of equity plan common stock     1,295 1,128
Repurchases and retirements of common stock     0 (14,828)
Principal payments on other borrowings       (36)
Net cash provided by (used in) financing activities     1,259 (13,736)
Foreign currency effect on cash and cash equivalents     440 (535)
Net increase (decrease) in cash and cash equivalents     50,988 (6,328)
Cash and cash equivalents at beginning of period     32,059 30,312
Cash and cash equivalents at end of period 83,047 23,984 83,047 23,984
Supplemental disclosures of cash flow information:        
Cash paid for interest     602 582
Cash paid for income taxes     2,057 597
Supplemental disclosures of non-cash investing and financing activities:        
Reclassification of convertible senior notes hedge and embedded conversion derivative to additional paid-in capital     0 42,821
Unrealized holding gain (loss) on available for sale investments $ 296 (828) $ 648 (1,098)
As Previously Reported        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Net income   1,013   4,137
Adjustments to reconcile net income to net cash provided by operating activities:        
Stock-based compensation expense       6,429
Amortization of intangible assets       4,525
Depreciation and amortization       555
Amortization of investment premiums & other       1,109
Accretion and amortization on debt securities       3,453
Net changes in estimated fair value of acquisition-related contingent consideration       (780)
Deferred taxes       (523)
Changes in assets and liabilities, net of acquisitions:        
Accounts receivable       (6,171)
Contract assets       345
Other assets       498
Accounts payable       3,769
Accrued payroll and related taxes       (4,693)
Deferred revenue       (3,126)
Other liabilities       159
Net cash provided by operating activities       9,686
Investing activities:        
Purchases of investments       (47,818)
Sales and maturities of investments       173,316
Acquisitions, net of cash acquired       (126,607)
Purchases of property and equipment       (634)
Net cash provided by (used in) investing activities       (1,743)
Financing activities:        
Proceeds from the issuance of equity plan common stock       1,128
Repurchases and retirements of common stock       (14,828)
Principal payments on other borrowings       (36)
Net cash provided by (used in) financing activities       (13,736)
Foreign currency effect on cash and cash equivalents       (535)
Net increase (decrease) in cash and cash equivalents       (6,328)
Cash and cash equivalents at beginning of period       30,312
Cash and cash equivalents at end of period   23,984   23,984
Supplemental disclosures of cash flow information:        
Cash paid for interest       582
Cash paid for income taxes       597
Supplemental disclosures of non-cash investing and financing activities:        
Reclassification of convertible senior notes hedge and embedded conversion derivative to additional paid-in capital       42,821
Unrealized holding gain (loss) on available for sale investments   (828)   (1,098)
Total Adjustments        
New Accounting Pronouncements or Change in Accounting Principle [Line Items]        
Net income   (578)   (578)
Adjustments to reconcile net income to net cash provided by operating activities:        
Stock-based compensation expense       0
Amortization of intangible assets       0
Depreciation and amortization       0
Amortization of investment premiums & other       0
Accretion and amortization on debt securities       0
Net changes in estimated fair value of acquisition-related contingent consideration       (590)
Deferred taxes       (240)
Changes in assets and liabilities, net of acquisitions:        
Accounts receivable       76
Contract assets       0
Other assets       (48)
Accounts payable       0
Accrued payroll and related taxes       0
Deferred revenue       911
Other liabilities       469
Net cash provided by operating activities       0
Investing activities:        
Purchases of investments       0
Sales and maturities of investments       0
Acquisitions, net of cash acquired       0
Purchases of property and equipment       0
Net cash provided by (used in) investing activities       0
Financing activities:        
Proceeds from the issuance of equity plan common stock       0
Repurchases and retirements of common stock       0
Principal payments on other borrowings       0
Net cash provided by (used in) financing activities       0
Foreign currency effect on cash and cash equivalents       0
Net increase (decrease) in cash and cash equivalents       0
Cash and cash equivalents at beginning of period       0
Cash and cash equivalents at end of period   0   0
Supplemental disclosures of cash flow information:        
Cash paid for interest       0
Cash paid for income taxes       0
Supplemental disclosures of non-cash investing and financing activities:        
Reclassification of convertible senior notes hedge and embedded conversion derivative to additional paid-in capital       0
Unrealized holding gain (loss) on available for sale investments   $ 0   $ 0