We show an $O(n\cdot L \cdot d^{L-1} + m + M_{\kappa,L})$-time algorithm finding all $\kappa$-MEMs between $Q$ and $G$ spanning exactly $L$ nodes in $G$, where $n$ is the total length of node labels, $d$ is the maximum degree of a node in $G$, $m = |Q|$, and $M_{\kappa,L}$ is the number of output MEMs.