Be $F_k$ a language over $\Sigma = \{0, 1, \#\}$ of the form:
$L_k = \{v\#uvw | u, v, e \in \{0, 1\}^*, |v| \leq k\}$.
Show that for each k: $L_k$ is regular by constructing a DFA for $L_k$.
The DFA is to be drwan for k=2.
My problem is that I don't know how to tackle this problem. I have only drawn DFAs for languages of the form $L_k = \{w | $some regular expression or textual condition$\}$ and I can't really find an example of such a language converted to a DFA.
Am I to draw a DFA for $v\#uvw$ or $\{0,1\}^*$?