Fair Value Measurements (Details) - USD ($) $ in Thousands	Sep. 30, 2020	Oct. 01, 2019	Sep. 30, 2019	Sep. 30, 2018
Fair Value, Recurring [Member] | Fair Value, Inputs, Level 1 [Member]
Deferred compensation plan assets
Trust Assets	$ 55		$ 16
Fair Value, Recurring [Member] | Fair Value, Inputs, Level 2 [Member]
Deferred compensation plan assets
Insurance	19,804		18,684
Foreign Currency Contract, Asset, Fair Value Disclosure	140		278
Liabilities:
Pension plan	(47,389)		(42,948)
Deferred compensation plan liabilities	(21,439)		(21,318)
Long‑term debt	(872,441)		(979,357)
Interest Rate Derivative Liabilities, at Fair Value	(4,669)
Foreign Currency Contracts, Liability, Fair Value Disclosure	47		154
Fair Value, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Liabilities:
Earn-outs related to acquisitions	(295)		(1,545)	$ (1,916)
Open Option Contracts Written, at Fair Value	(7,739)
Fair Value, Recurring [Member] | Cash | Fair Value, Inputs, Level 1 [Member]
Assets:
Fair value of plan assets	15,061		14,607
Fair Value, Recurring [Member] | US Government Agencies Debt Securities [Member]
Assets:
Plan assets at net asset value	4,924		4,703
Fair Value, Recurring [Member] | Liability Driven Investment [Member]
Assets:
Plan assets at net asset value	3,604		3,261
Fair Value, Recurring [Member] | Guernsey Unit Trust [Member]
Assets:
Plan assets at net asset value	1,881		997
Fair Value, Recurring [Member] | Global Absolute Return [Member]
Assets:
Plan assets at net asset value	2,060		1,957
Other Current Liabilities [Member] | Fair Value, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Liabilities:
Earn-outs related to acquisitions	(295)		(611)	(770)
Open Option Contracts Written, at Fair Value	0
Other Noncurrent Liabilities [Member] | Fair Value, Recurring [Member] | Fair Value, Inputs, Level 3 [Member]
Liabilities:
Earn-outs related to acquisitions	0		$ (934)	$ (1,146)
Frontier [Member]
Fair Value, Assets and Liabilities Measured on Recurring and Nonrecurring Basis [Line Items]
Business Acquisition, Percentage Of Voting Interest Remaining		40.00%
Frontier [Member] | Other Current Liabilities [Member]
Liabilities:
Open Option Contracts Written, at Fair Value	(506)
Frontier [Member] | Other Noncurrent Liabilities [Member]
Liabilities:
Open Option Contracts Written, at Fair Value	$ (6,661)