Only the 2 kronen on  dinar and 4 kronen on 1 dinar had variants without the overprint. It is as yet ambiguous as to whether the overprinted version was issued before or after.
Only specific variants of the dinar, namely those with 2 kronen and 4 kronen, lacked overprinting. The timing of the overprinted version's introduction relative to these unique designs remains ambiguous.