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Basis of Presentation - Cash and Cash Equivalents (Details) - USD ($) $ in Thousands | Sep. 30, 2024 | Sep. 30, 2023
--- | --- | ---
Fair Value, Inputs, Level 1 |  |
Cash and Cash Equivalents [Abstract] |  |
Fair value of cash and cash equivalents | $ 53,688 | $ 334,633
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Fair value of cash and cash equivalents | 53,688 | 334,633
Long-Term Debt, Fair Value | 0 | 0
Contingent considerations | 0 | 0
Fair Value, Inputs, Level 1 | Deferred Compensation, Share-Based Payments |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Other Deferred Compensation Arrangements, Liability, Current and Noncurrent | 2,053 | 0
Fair Value, Inputs, Level 1 | Deferred Bonus and Profit Sharing Arrangement, Individual Contract, Type of Deferred Compensation [Domain] |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Deferred Compensation Plan Assets | 896 | 0
Fair Value, Inputs, Level 1 | Foreign Exchange Contract |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 0 | 0
Fair Value, Inputs, Level 1 | Derivative Contracts |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 0 | 0
Fair Value, Inputs, Level 1 | Revolving Credit Facility |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Revolving loan | 0 | 0
Fair Value, Inputs, Level 2 |  |
Cash and Cash Equivalents [Abstract] |  |
Fair value of cash and cash equivalents | 0 | 0
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Fair value of cash and cash equivalents | 0 | 0
Long-Term Debt, Fair Value | 393,750 | 416,250
Contingent considerations | 0 | 0
Fair Value, Inputs, Level 2 | Deferred Compensation, Share-Based Payments |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Other Deferred Compensation Arrangements, Liability, Current and Noncurrent | 0 | 0
Fair Value, Inputs, Level 2 | Deferred Bonus and Profit Sharing Arrangement, Individual Contract, Type of Deferred Compensation [Domain] |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Deferred Compensation Plan Assets | 0 | 0
Fair Value, Inputs, Level 2 | Foreign Exchange Contract |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities |  | 9,327
Fair Value, Inputs, Level 2 | Deferred Income Tax Charge |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 30,059 |
Fair Value, Inputs, Level 2 | Derivative Contracts |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 14,199 | 42,769
Fair Value, Inputs, Level 2 | Revolving Credit Facility |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Revolving loan | 75,038 | 150,038
Fair Value, Inputs, Level 3 |  |
Cash and Cash Equivalents [Abstract] |  |
Fair value of cash and cash equivalents | 0 | 0
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Fair value of cash and cash equivalents | 0 | 0
Long-Term Debt, Fair Value | 0 | 0
Contingent considerations | 6,587 | 5,400
Fair Value, Inputs, Level 3 | Deferred Compensation, Share-Based Payments |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Other Deferred Compensation Arrangements, Liability, Current and Noncurrent | 0 | 0
Fair Value, Inputs, Level 3 | Deferred Bonus and Profit Sharing Arrangement, Individual Contract, Type of Deferred Compensation [Domain] |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Deferred Compensation Plan Assets | 0 | 0
Fair Value, Inputs, Level 3 | Foreign Exchange Contract |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 0 | 0
Fair Value, Inputs, Level 3 | Derivative Contracts |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Derivative instruments, assets and liabilities | 0 | 0
Fair Value, Inputs, Level 3 | Revolving Credit Facility |  |
Fair Value, Balance Sheet Grouping, Financial Statement Captions [Line Items] |  |
Revolving loan | $ 0 | $ 0

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- Definition Fair value portion of currency on hand as well as demand deposits with banks or financial institutions. Includes other kinds of accounts that have the general characteristics of demand deposits. Also includes short-term, highly liquid investments that are both readily convertible to known amounts of cash and so near their maturity that they present insignificant risk of changes in value because of changes in interest rates. + References Reference 1: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (b) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 Reference 2: http://www.xbrl.org/2009/role/commonPracticeRef -Topic 820 -SubTopic 10 -Name Accounting Standards Codification -Section 50 -Paragraph 2 -Subparagraph (a) -Publisher FASB -URI https://asc.fasb.org/1943274/2147482106/820-10-50-2 + Details
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