Default equilibrium-constant?

Let's say we have the reaction 2H2 + O2 -> 2H2O. The equilibrium constant for this reaction then is: K1=[H2O]2]/([H2]2*[O2]).

But the reaction can also be written as H2 + 0.5O2 -> H2O, and with the equilibrium constant becoming K2 = [H2O]1]/([H2]1*[O2]0.5)=K10.5

This phenomena with the coefficients goes generally for all reactions. So, what K is the default one? Is it the one where most coefficients are 1 (K2), or is it when all coefficients are at their smallest, while remaining integers (K1)? Or something else?