[DCP-o-matic] Upres to 4K

Hi all. I'm making a DCP of compilation of short films. Half the films are 4K source, the other half are 2K. If I make the DCP as 4K, the 2K films will get uprezzed to 4K, but the majority of cinemas will probably only have 2K projectors, so will downres to 2K again. Will that result in the 2K films looking worse than they would have if the DCP was made 2K in the first place? i.e. This would involve 2 translations: (1) DCP-o-matic 2K -> 4K scaling and (2) J2K decoding discarding a resolution level. Are the two translations a good mirror of each other? Or do they work in different ways so it could result in the 2K film looking less sharp than if DCP had been encoded in 2K in the first place? Obviously, the 4K films would look less sharp if encoded as 2K. But what I'm wondering is whether I need to make both 2K and 4K DCPs so the films can be presented optimally in all cinemas, or whether just a 4K DCP will cover all cases. Hope this makes some kind of sense! Jim