pricing - How to derive the price of a square-or-nothing call option?

At maturity $T$, the holder of a "square-or-nothing" call option written on an underlying $S_t$ receives a payoff of the form

$$\phi(S_T) = \frac{S_T^2}{K} \pmb{1}_{\{S_T \geq K\}} = \begin{cases}\frac{S_T^2}{K}, &\text{ if }\ \ S_T \geq K, \\ 0, & \text{otherwise}.\end{cases}$$

Assume a Black-Scholes diffusion framework where the underlying's risk-neutral drift $\mu$ and volatility $\sigma$ are given.

Can one derive a closed-form pricing formula for such an option?