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Debt (Details)
12 Months Ended
May 15, 2019
Sep. 30, 2018
USD ($)
Sep. 30, 2017
USD ($)
Sep. 30, 2016
USD ($)
bank
Sep. 13, 2018
USD ($)
May 31, 2016
USD ($)
Debt Instrument [Line Items]            
Senior Notes   $ 500,000,000 $ 500,000,000     $ 500,000,000
Long-term Debt, Gross   648,125,000 718,125,000      
Unamortized Debt Issuance Expense   (4,857,000) (5,719,000)      
debt net of unamortized debt issuance cost   643,268,000 712,406,000      
Debt Instrument, Interest Rate, Stated Percentage           6.00%
Debt Instrument, Fair Value Disclosure   $ 521,200,000        
Voting interest in domestic subsidiaries pledged against credit facility   100.00%        
Voting interest in foreign subsidiaries pledged against credit facility   65.00%        
Investment limit in foreign subsidiaries   $ 100,000,000        
Cash investment limit for acquisition of business   $ 200,000,000        
Minimum fixed charge coverage ratio allowed under debt covenant   3.00        
Leverage ratio, actual   2.36        
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio, actual   0.58        
Fixed charge coverage ratio, actual   6.18        
Credit facility, origination costs   $ 2,900,000   $ 6,900,000    
Credit facility, periodic interest payment   $ 39,800,000 $ 38,900,000 $ 13,300,000    
Credit facility, average interest rate during period   5.20% 4.90% 3.00%    
Maximum [Member]            
Debt Instrument [Line Items]            
Credit facility, variable interest rate, length of time between updates   180 days        
Minimum [Member]            
Debt Instrument [Line Items]            
Credit facility, variable interest rate, length of time between updates   30 days        
Term Loan [Member]            
Debt Instrument [Line Items]            
Number of banks in credit agreement | bank       16    
Line of Credit [Member]            
Debt Instrument [Line Items]            
Credit facility, borrowings outstanding   $ 148,125,000 $ 218,125,000      
Credit facility, current maximum amount   $ 700,000,000     $ 600,000,000  
Credit facility, revolving loan, basis spread on federal funds effective rate   0.50%        
Credit facility, revolving loan, basis spread on adjusted LIBOR   1.00%        
Maximum leverage ratio allowed under debt covenant   4.50        
Debt Instrument, Covenant Compliance, Senior Debt Leverage Ratio   3.0        
Line of Credit [Member] | Maximum [Member]            
Debt Instrument [Line Items]            
Credit facility, revolving loan, commitment fees percentage   0.30%        
Line of Credit [Member] | Minimum [Member]            
Debt Instrument [Line Items]            
Credit facility, revolving loan, commitment fees percentage   0.175%        
LIBOR for Eurodollar-Based Borrowings [Member] | Line of Credit [Member] | Maximum [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Basis Spread on Variable Rate   1.75%        
LIBOR for Eurodollar-Based Borrowings [Member] | Line of Credit [Member] | Minimum [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Basis Spread on Variable Rate   1.25%        
Base Rate [Member] | Line of Credit [Member] | Maximum [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Basis Spread on Variable Rate   0.75%        
Base Rate [Member] | Line of Credit [Member] | Minimum [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Basis Spread on Variable Rate   0.25%        
Revolving Loan, Reset December 17, 2015 | Term Loan [Member]            
Debt Instrument [Line Items]            
Credit facility, term loan, interest rate at period end   3.80%        
Scenario, Forecast [Member]            
Debt Instrument [Line Items]            
Debt Instrument, Redemption Price, Percentage 101.00%          
Other Noncurrent Assets [Member] | Line of Credit [Member]            
Debt Instrument [Line Items]            
Unamortized Debt Issuance Expense   $ (3,800,000) $ (2,000,000)      
Foreign Subsidiary [Member] | Line of Credit [Member]            
Debt Instrument [Line Items]            
Credit facility, borrowings outstanding   $ 110,000,000