Singular Values & the SVD · Challenge problem

Let $A = \begin{pmatrix}3 & 0\\4 & 5\end{pmatrix}$, $B = \begin{pmatrix}1 & 1\\0 & 1\end{pmatrix}$, and let $K = A\otimes B$ be their $4\times 4$ Kronecker product. Find the nuclear norm $\|K\|_* = \sum\sigma_i(K)$.