Breeden-Litzenberger

Consider a risky asset $(S_t)$ under the risk-neutral measure $\mathbb{Q}$ with deterministic interest rate $r$. Let $B(t,T) = e^{-r(T-t)}$ denote the zero-coupon bond price.

Let $C_t(K)$ be the price at time $t$ of a European call with maturity $T$ and strike $K$, and let $D_t(K)$ be the price of a digital call with the same maturity and strike, with payoff .

Question: Express $D_t(K)$ in terms of $C_t(K)$ and the strike $K$.