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Share-Based Compensation - Options by Exercise Price (Details)
12 Months Ended
Sep. 30, 2019
$ / shares
shares
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Number of Outstanding Options | shares 1,684,378
Weighted Average Exercise Price $ 37.59
Weighted Average Remaining Term (in years) 4 years 7 months 13 days
$0 - $5,00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 0.00
Exercise Price Range, Upper Range Limit $ 5.00
Number of Outstanding Options | shares 0
$5.00 - $10.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 5.00
Exercise Price Range, Upper Range Limit $ 10.00
Number of Outstanding Options | shares 0
$10.00 - $15.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 10.00
Exercise Price Range, Upper Range Limit $ 15.00
Number of Outstanding Options | shares 0
$15.00 - $20.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 15.00
Exercise Price Range, Upper Range Limit $ 20.00
Number of Outstanding Options | shares 0
$20.00 - $25.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 20.00
Exercise Price Range, Upper Range Limit $ 25.00
Number of Outstanding Options | shares 0
$25.00 - $30.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 25.00
Exercise Price Range, Upper Range Limit $ 30.00
Number of Outstanding Options | shares 564,000
Weighted Average Exercise Price $ 25.91
Weighted Average Remaining Term (in years) 2 years 4 months 13 days
$30.00 - $35.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 30.00
Exercise Price Range, Upper Range Limit $ 35.00
Number of Outstanding Options | shares 32,881
Weighted Average Exercise Price $ 31.37
Weighted Average Remaining Term (in years) 3 months 11 days
$35.00 - $40.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 35.00
Exercise Price Range, Upper Range Limit $ 40.00
Number of Outstanding Options | shares 213,830
Weighted Average Exercise Price $ 39.33
Weighted Average Remaining Term (in years) 2 years 5 months 5 days
$40.00 - $45.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 40.00
Exercise Price Range, Upper Range Limit $ 45.00
Number of Outstanding Options | shares 871,667
Weighted Average Exercise Price $ 44.91
Weighted Average Remaining Term (in years) 6 years 9 months 11 days
$45.00 - $50.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 45.00
Exercise Price Range, Upper Range Limit $ 50.00
Number of Outstanding Options | shares 0
$50.00 - $55.00 [Member]  
Share-based Compensation, Shares Authorized under Stock Option Plans, Exercise Price Range [Line Items]  
Exercise Price Range, Lower Range Limit $ 50.00
Exercise Price Range, Upper Range Limit $ 55.00
Number of Outstanding Options | shares 0