Assuming the op amp to he ideal, derive an expression for the closed-loop gain $v_0 / v_1$ of the circuit shown in the provided circuit image. Use this circuit to design an inverting amplifier with a gain of 100 and an input resistance of $1 \mathrm{M} \Omega$. Assume that for practical reasons it is required not to use resistors greater than $1 \mathrm{M} \Omega$.