Share-based Compensation - Additional Information (Details) € / shares in Units, € in Thousands	1 Months Ended	12 Months Ended
	Mar. 31, 2023 shares Tranche € / shares	Sep. 30, 2023 EUR (€)
Disclosure of terms and conditions of share-based payment arrangement [line items]
Recognized share-based compensation expense | €		€ 65,394
Management Investment Plan | BK LC Manco GmbH & Co. KG
Disclosure of terms and conditions of share-based payment arrangement [line items]
Number of shares granted | shares	1,197,100
Number of tranches | Tranche	5
Percentage of shares granted to each tranche	20.00%
Number of shares forfeited/ canceled/ settled | shares	0
Granted shares vesting period	4 years
Percentage of shares granted vesting after each year of service	20.00%
Percentage of shares granted that vests with occurrence of an exit	20.00%
Minimum required period for exit event to occur after the grant	12 months
Weighted average fair value of the awards granted | € / shares	€ 57.57
Ordinary redeemable share price | € / shares	€ 72.23
Management Investment Plan | BK LC Manco GmbH & Co. KG | First Tranche
Disclosure of terms and conditions of share-based payment arrangement [line items]
Percentage of grants included in grant date fair value, accounted after occurrence of exit event	20.00%