L(0,m) = 0 for all m, and the unique optimal set of coins is the empty set.
L(1,m) = m for all m, and the unique optimal set of coins is {1}.
L(k,0) = 0 for all k, and one can choose the set of coins arbitrarily.
L(k,1) = k for all k, and the unique optimal set of coins is {1,2,...,k}.