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Fair Value Measurements - Summary of Financial Assets and Liabilities Measured at Fair Value (Details) - USD ($) $ in Thousands	Dec. 31, 2024	Sep. 30, 2024
Assets:
Interest rate swap contract	$ 824	$ 716
Liabilities:
Contingent consideration liabilities	55,494	81,311
Level 2 [Member]
Assets:
Interest rate swap contract	824	716
Level 3 [Member]
Liabilities:
Contingent consideration liabilities	$ 55,494	$ 81,311

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- Definition

Fair value portion of asset recognized for present right to economic benefit.

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- Definition

Fair value of financial and nonfinancial obligations.

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