Beyond binary Merkle trees: Alice can use a binary Merkle tree to commit to a set of elements S $=\{$T$1,...,$ Tn$\}$ so that later she can prove to Bob that some Ti is in S using a proof containing at most $$log n$$ hash values. In this question your goal is to explain how to do the same using a kary tree, that is$,$ where every non$-$leaf node has up to k children. The hash value for every non$-$leaf node is computed as the hash of the concatenation of the values of its children. a$.$ Suppose S $=\{$T$1,...,$ T$9\}.$ Explain how Alice computes a commitment to S using a ternary Merkle tree $($i$.$e$.$ k $=3).$ How can Alice later prove to Bob that T$4$ is in S $.$ b$.$ Suppose S contains n elements. What is the length of the proof that proves that some Ti is in S$,$ as a function of n and k$?$ c$.$ For large n$,$ what is the proof size overhead of a kary tree compared to a binary tree? Can you think of any advantage to using a k $>2?($Hint: consider computation cost$)$