Stock-Based Compensation - Schedule Of Common Stock Available For Issuance Under The Equity Incentive Plans (Details)	Jun. 30, 2026 shares
Share-Based Payment Arrangement [Abstract]
Outstanding stock awards	21,658,848
Reserved for future award grants	2,769,357
Reserved for future ESPP purchases	230,311
Total	24,658,516

Sahre Based Compensation Arrangement By Share Based Payment Award Awards Outstanding

No definition available.

Name:	kod_SahreBasedCompensationArrangementByShareBasedPaymentAwardAwardsOutstanding
Namespace Prefix:	kod_
Data Type:	xbrli:sharesItemType
Balance Type:	na
Period Type:	instant