2023 AMC 12B Problem 8

How many nonempty subsets B of \{0,1,2,3,\ldots,12\} have the property that the number of elements in B is equal to the least element of B? For example, B=\{4,6,8,11\} satisfies the condition.

\textbf{(A)} 256 \qquad \textbf{(B)} 136 \qquad \textbf{(C)} 108 \qquad \textbf{(D)} 144 \qquad \textbf{(E)} 156

Full credit goes to MAA for authoring these problems. These problems were taken on the AOPS website.