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Stockholders' Equity (Tables) | 12 Months Ended
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Sep. 30, 2023
Stockholders' Equity Note [Abstract] |
Summary of accumulated other comprehensive income (loss) | The following is a summary of the components of accumulated other comprehensive income (loss), net of tax, at September 30, 2023, 2022 and 2021 (in thousands):
​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ |  | ​ | ​ |  | Unrealized |  | ​ | ​ | ​ | ​ |  | ​ | ​
​ | ​ | ​ | ​ | ​ | Gains (Losses) | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | ​ | ​ | ​ | on Available- | ​ | ​ | ​ | ​ | ​ | ​ | ​ | ​
​ | ​ | Currency | ​ | for-Sale | ​ | Gains (Losses) | ​ | Pension | ​ |  | ​
​ | ​ | Translation | ​ | Securities | ​ | on Derivative asset | ​ | Liability | ​ |  | ​
​ | ​ | Adjustments | ​ | Net of tax | ​ | Net of tax | ​ | Adjustments | ​ | Total
Balance at September 30, 2020 | ​ | $ | 23,061 | ​ |  | (1) | ​ |  | — | ​ |  | (1,141) | ​ |  | 21,919
Other comprehensive income (loss) before reclassifications | ​ |  | (2,922) | ​ |  | — | ​ |  | — | ​ |  | 333 | ​ |  | (2,589)
Amounts reclassified from accumulated other comprehensive income (loss) | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 21 | ​ |  | 21
Balance at September 30, 2021 | ​ |  | 20,139 | ​ |  | (1) | ​ |  | — | ​ |  | (787) | ​ |  | 19,351
Other comprehensive income (loss) before reclassifications | ​ |  | (169,266) | ​ |  | (10,908) | ​ |  | 93,020 | ​ |  | 412 | ​ |  | (86,742)
Amounts reclassified from accumulated other comprehensive income (loss) | ​ |  | (16,567) | ​ |  | — | ​ |  | — | ​ |  | 42 | ​ |  | (16,525)
Balance at September 30, 2022 | ​ |  | (165,694) | ​ | ​ | (10,909) | ​ | ​ | 93,020 | ​ | ​ | (333) | ​ |  | (83,916)
Other comprehensive income (loss) before reclassifications | ​ |  | 77,246 | ​ |  | 5,774 | ​ |  | (61,533) | ​ |  | (104) | ​ |  | 21,383
Amounts reclassified from accumulated other comprehensive income (loss) | ​ |  | — | ​ |  | — | ​ |  | — | ​ |  | 107 | ​ |  | 107
Balance at September 30, 2023 | ​ | $ | (88,448) | ​ | $ | (5,135) | ​ | $ | 31,487 | ​ | $ | (330) | ​ | $ | (62,426)

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