There exists a real number \(k\) such that the equation \(\begin{pmatrix} -1 \\ -2 \end{pmatrix} + t \begin{pmatrix} \phantom -3 \\ -2 \end{pmatrix} = \begin{pmatrix} 5 \\ 0 \end{pmatrix} + s \begin{pmatrix} 4 \\ k \end{pmatrix}\)
does not have any solutions in t and s. Find k.