Design an emitter-coupled pair of the type shown in the provided circuit image. Assume $I_{\text {TAIL }}=0$ and select values of $R_C$ and $R_{\text {TAIL }}$ to give a differential input resistance of $2 \mathrm{M} \Omega$, a differential voltage gain of 500 , and a CMRR of 500. Assume that the dc common-mode input voltage is zero. Neglect $r_b, r_\mu$, and $r_o$.