terminology - Sufficient conditions for a mapping to be canonical in Hamiltonian Mechanics

My professor mentioned: A simple way of testing whether a mapping $(q,p)$ to $(Q,P)$ is canonical is by examining:

$$P · dQ − p · dq$$

and if it equals to $dA$ (a differential) then it is canonical.

However, I'm wondering why is this the case, since the requirements for canonical map is that at first is $$P ·dQ − Kdt = p·dq − Hdt + dS$$ (so that the closed contour integral of $P ·dQ − Kdt$ to equal that of $p·dq − Hdt$. Then what about the $Kdt$ and $Hdt$?