Compute the flux of the vector field $\vec F = z\vec k$ through the parameterized surface $S$, which is oriented toward the $z$-axis and given, for $0\leq s \leq 1, \ \ 0\leq t\leq 4$, by $$x = 2 s + 3 t, \quad y = 2 s - 3 t, \quad z = s^2+t^2.$$

flux =