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Long-Term Debt, Net - Additional Information (Details)
6 Months Ended 12 Months Ended
Sep. 30, 2023
USD ($)
$ / shares
May 08, 2023
USD ($)
Oct. 03, 2022
USD ($)
Feb. 18, 2020
USD ($)
day
$ / shares
Feb. 13, 2020
USD ($)
$ / shares
shares
Sep. 30, 2020
USD ($)
Sep. 30, 2023
USD ($)
$ / shares
Sep. 30, 2022
USD ($)
Sep. 30, 2021
USD ($)
Oct. 01, 2022
USD ($)
Debt Instrument [Line Items]                    
Long-term debt, less current portion and debt issuance costs, net $ 385,081,000           $ 385,081,000 $ 287,020,000    
Decrease in additional paid-in-capital (249,688,000)           (249,688,000) (241,958,000)    
Accumulated earnings (12,944,000)           (12,944,000) (23,582,000)    
Amortization of deferred debt issuance costs             1,514,000 1,046,000 $ 968,000  
Debt issuance costs, net 4,424,000           4,424,000 2,554,000    
Exchangeable notes, fair value 108,506,000           108,506,000      
Payments for note hedge transactions         $ 28,676,000          
Debt issuance costs incurred             3,079,000 0 $ 0  
Cumulative Effect, Period of Adoption, Adjustment | Accounting Standards Update 2020-06                    
Debt Instrument [Line Items]                    
Long-term debt, less current portion and debt issuance costs, net                   $ 11,933,000
Decrease in additional paid-in-capital                   23,382,000
Accumulated earnings                   $ 11,449,000
1.0% Exchangeable Senior Notes due 2025                    
Debt Instrument [Line Items]                    
Repayments of convertible debt           $ 17,414,000        
1.0% Exchangeable Senior Notes due 2025 | Exchangeable Notes                    
Debt Instrument [Line Items]                    
Original principal amount       $ 138,000,000            
Stated interest rate       1.00%            
Net proceeds from the sale of the exchangeable notes       $ 132,762,000            
Long-term debt 117,000,000           117,000,000 104,557,000    
Amortization of deferred debt issuance costs             949,000 666,000    
Debt issuance costs, net 1,501,000           1,501,000      
Debt aggregate repurchase amount           21,000,000        
Debt interest, repurchase amount           $ 24,000        
1.0% Exchangeable Senior Notes due 2025 | Exchangeable Notes | In Event of Fundamental Change                    
Debt Instrument [Line Items]                    
Repurchase price as percent of face value of notes       100.00%            
1.0% Exchangeable Senior Notes due 2025 | Exchangeable Notes | February 20, 2023 to 47th Scheduled Trading Day Immediately Preceding the Maturity Date                    
Debt Instrument [Line Items]                    
Repurchase price as percent of face value of notes       100.00%            
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit                    
Debt Instrument [Line Items]                    
Long-term debt $ 272,505,000           $ 272,505,000 0    
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | One, Two, Three, Or Six Month SOFR                    
Debt Instrument [Line Items]                    
Basis spread on variable rate 3.00%                  
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | One, Two, Three, Or Six Month SOFR | Minimum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   2.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | One, Two, Three, Or Six Month SOFR | Maximum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   3.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1%                    
Debt Instrument [Line Items]                    
Basis spread on variable rate 2.00%                  
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1% | Minimum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   1.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1% | Maximum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   2.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility                    
Debt Instrument [Line Items]                    
Revolving line of credit borrowing capacity   $ 450,000,000                
Optional addition to borrowing capacity   $ 100,000,000                
Consolidation basis   1                
Debt covenant, minimum consolidated interest coverage ratio 4.39 3         4.39      
Debt covenant, maximum total leverage ratio 3.77 5         3.77      
Commitment fee percentage 0.30%                  
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Minimum                    
Debt Instrument [Line Items]                    
Commitment fee percentage   0.15%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Maximum                    
Debt Instrument [Line Items]                    
Commitment fee percentage   0.30%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | One, Two, Three, Or Six Month SOFR                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   0.10%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Adjusted Term SOFR                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   0.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Federal Funds Rate                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   0.50%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Secured Overnight Financing Rate SOFR                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   1.00%                
Revolving lines of credit to banks under the 2023 Senior Secured Credit Facility | Line of Credit | Revolving Credit Facility | Base Rate                    
Debt Instrument [Line Items]                    
Basis spread on variable rate   1.00%                
2019 Senior Secured Credit Facility | Line of Credit                    
Debt Instrument [Line Items]                    
Long-term debt $ 0           $ 0 $ 185,017,000    
Revolving line of credit borrowing capacity     $ 375,000,000              
Optional addition to borrowing capacity     $ 50,000,000              
Write off of deferred debt issuance cost             $ 203,000      
2019 Senior Secured Credit Facility | Line of Credit | Minimum                    
Debt Instrument [Line Items]                    
Commitment fee percentage     0.15%              
2019 Senior Secured Credit Facility | Line of Credit | Maximum                    
Debt Instrument [Line Items]                    
Commitment fee percentage     0.30%              
2019 Senior Secured Credit Facility | Line of Credit | Federal Funds Rate                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     0.50%              
2019 Senior Secured Credit Facility | Line of Credit | Secured Overnight Financing Rate SOFR                    
Debt Instrument [Line Items]                    
Adjustment in addition to basis spread     0.10%              
2019 Senior Secured Credit Facility | Line of Credit | Secured Overnight Financing Rate SOFR | Minimum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     2.25%              
2019 Senior Secured Credit Facility | Line of Credit | Secured Overnight Financing Rate SOFR | Maximum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     3.25%              
2019 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1%                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     1.00%              
Adjustment in addition to basis spread     0.10%              
2019 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1% | Minimum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     0.25%              
2019 Senior Secured Credit Facility | Line of Credit | SOFR Plus 1% | Maximum                    
Debt Instrument [Line Items]                    
Basis spread on variable rate     1.25%              
2019 Senior Secured Credit Facility | Line of Credit | Letter of Credit Fee | Maximum                    
Debt Instrument [Line Items]                    
Commitment fee percentage     3.25%              
Additional Paid-In Capital                    
Debt Instrument [Line Items]                    
Equity component of exchangeable notes, net of issuance costs and deferred taxes       $ 28,662,000            
Class A Common Stock                    
Debt Instrument [Line Items]                    
Exchangeable notes, exchange price per share (in USD per share) | $ / shares $ 40.87     $ 40.87     $ 40.87      
Warrants outstanding (in shares) | shares         3,376,391          
Warrants sold in connection with the issuance of the Exchangeable notes (in USD per share) | $ / shares         $ 62.88          
Proceeds from offering and sale of warrants         $ 14,669,000          
Class A Common Stock | 1.0% Exchangeable Senior Notes due 2025 | Exchangeable Notes                    
Debt Instrument [Line Items]                    
Exchangeable notes, exchange rate, shares per $1000       0.0244666            
Class A Common Stock | 1.0% Exchangeable Senior Notes due 2025 | Exchangeable Notes | February 20, 2023 to 47th Scheduled Trading Day Immediately Preceding the Maturity Date                    
Debt Instrument [Line Items]                    
Threshold exchange price as percent of closing price per share to allow redemption       130.00%            
Threshold trading days closing price for stock must exceed exchange price | day       20