Reciprocal SDE

Let $W_t$ be a standard Brownian Motion. Suppose that $X_t$ is some process such that $\dfrac{1}{X_t}$ satisfies the SDE $d\left(\dfrac{1}{X_t}\right) = \dfrac{1}{X_t}\left(2dt - dW_t\right)$. The SDE that $X_t$ satisfies is in the form $dX_t = X_t(adt + bdW_t)$ for some integers $a$ and $b$. Find $ab$.