Fair Value Measurements (Details) - USD ($) $ in Thousands	Jun. 30, 2021	Apr. 08, 2021	Sep. 30, 2020
Assets:
Mutual Funds	$ 17,964
Fair Value, Measurements, Recurring | Quoted Market Prices in Active Markets (Level 1)
Assets:
Cash	1,240
Deferred compensation plan assets
Cash			$ 55
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 2
Assets:
Foreign currency forward contracts	59		140
Deferred compensation plan assets
Mutual Funds			19,804
Liabilities:
Pension plan	(48,524)		(47,389)
Deferred compensation plan liabilities	(23,980)		(21,439)
Long‑term debt	(799,922)		(872,441)
Interest Rate Derivative Liabilities, at Fair Value	(376)		(4,669)
Foreign currency forward contracts	(120)		(47)
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 2 | Other Current Liabilities | Designated as Hedging Instrument
Deferred compensation plan assets
Interest rate cap	2,443		0
Liabilities:
Interest Rate Derivative Liabilities, at Fair Value	(376)		(4,669)
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 3
Liabilities:
Earn-outs related to acquisitions	(1,056)		(295)
Option and purchase right	(6,249)		(7,739)
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 3 | Other Current Liabilities
Liabilities:
Earn-outs related to acquisitions	(1,056)		(1,056)
Fair Value, Measurements, Recurring | Fair Value, Inputs, Level 3 | Other Noncurrent Liabilities
Liabilities:
Option and purchase right	6,249		7,739
Fair Value, Measurements, Recurring | Cash | Quoted Market Prices in Active Markets (Level 1)
Assets:
Defined benefit plan, fair value of plan assets	448		15,061
Fair Value, Measurements, Recurring | US Government Agencies Debt Securities
Assets:
Plan assets at net asset value	2,557		4,924
Fair Value, Measurements, Recurring | Liability Driven Investment
Assets:
Plan assets at net asset value	5,930		3,604
Fair Value, Measurements, Recurring | Guernsey Unit Trust
Assets:
Plan assets at net asset value	2,381		1,881
Fair Value, Measurements, Recurring | Global Absolute Return
Assets:
Plan assets at net asset value	2,275		$ 2,060
Fair Value, Measurements, Recurring | Hedge Funds, Multi-strategy
Assets:
Plan assets at net asset value	$ 15,303
Frontier
Liabilities:
Option and purchase right		$ (1,490)