A student sits on a stool that is free to rotate with negligible friction about a vertical axis. Initially, the student is rotating with an angular velocity \(\omega_i\) while holding weights in their outstretched arms. The initial rotational inertia of the student-stool-weights system is \(I_i\). When the student pulls the weights inward toward the axis, the rotational inertia of the system decreases to \(I_f = \dfrac{1}{3} I_i\). Which of the following expressions correctly relates the final rotational kinetic energy \(K_f\) of the system to the initial rotational kinetic energy \(K_i\)?