Nature of Business and Summary of Significant Accounting Policies - Estimated Useful Life of Property and Equipment (Details)	12 Months Ended
	Sep. 30, 2022
Data processing equipment and software | Minimum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	3 years
Data processing equipment and software | Maximum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	6 years
Office furniture and equipment | Minimum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	3 years
Office furniture and equipment | Maximum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	7 years
Leasehold improvements
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	Shorter of estimated useful life or lease term
Equipment under capital lease
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	Shorter of estimateduseful life or lease term
Software Development | Minimum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	2 years
Software Development | Maximum
Property, Plant and Equipment [Line Items]
Property and equipment, estimated useful life	3 years