For the digits $A, D, T$ and $Y$
$$\begin{array}{r}
\text{TYT} \\
\text{AYT} \\
+ \quad \text{YDT} \\
\hline 2024
\end{array}$$
an addition operation is given.
$\text{TYT} < \text{AYT}$
According to this, what is the product $Y \cdot D \cdot T$?
A) 48
B) 64
C) 80
D) 96
E) 112