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Share-Based Compensation Plans - Weighted Average Assumptions (Details) - Stock option - $ / shares
12 Months Ended
Sep. 30, 2021
Sep. 30, 2020
Sep. 30, 2019
Share-based Compensation Arrangement by Share-based Payment Award, Fair Value Assumptions and Methodology [Abstract]      
Weighted-average grant date fair value (in dollars per share) $ 51.92 $ 39.68 $ 27.34
Expected term (in years) 6 years 8 months 26 days 6 years 11 months 15 days 6 years 10 months 9 days
Expected volatility 40.00% 32.00% 26.00%
Risk-free rate of return 0.70% 1.60% 2.80%
Dividend yield 1.20% 1.30% 1.60%