GATE EC 2024 Set 1 Q41 — Combinatorial Circuits

In the circuit shown below, the transistors $M_{1}$ and $M_{2}$ are biased in saturation. Their small signal transconductances are $g_{m 1}$ and $g_{m 2}$ respectively. Neglect body effect, channel length modulation and intrinsic device capacitances.

Assuming that capacitor $C_{1}$ is a short circuit for $\mathrm{AC}$ analysis, the exact magnitude of small signal voltage gain $\left|\frac{v_{\text{out }}}{v_{\text{in }}}\right|$ is