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 |