Calculate the flux integral. $\int_S (2 \vec i + 3 z\vec k)\cdot d\vec A$ where $S$ is $z = x^2+y^2$ with $0\le x\le 1, 0\le y\le 3$, oriented upward.

$\int_S (2 \vec i + 3 z\vec k)\cdot d\vec A =$