A uniform solid cylinder of mass \(M\) and radius \(R\) is connected at its frictionless central axle to an ideal horizontal spring of force constant \(k\), with the opposite end of the spring fixed to a rigid vertical wall. The cylinder rolls without slipping along a horizontal surface. The cylinder is pulled horizontally until the spring is stretched by a distance \(A\) from its unstretched equilibrium position and is then released from rest. In terms of \(k\) and \(A\), what is the maximum rotational kinetic energy of the cylinder during the subsequent motion?