Cylinder over Step

A cylinder of mass $M$ and radius $R$ sits against a step of height $h = R/2$ as shown above. A force $\vec{F}$ is applied at right angles to the line connecting the corner of the step and the center of the cylinder. All answers should be in terms of $M$, $R$, $g$.

a) Find the minimum value of $\vert\vec{F}\vert$ that will roll the cylinder over the step if the cylinder does not slide on the corner.

b) What is the force exerted by the corner (magnitude and direction) when that force $\vec{F}$ is being exerted on the center?