Mahlo classes for first-order reflections

In this note we axiomatize the ${\mathrm{\Pi }}_{k+1}$-consequences in the set theory $\mathsf{K}\mathsf{P}{\mathrm{\Pi }}_N$ for ${\mathrm{\Pi }}_N$-reflecting universes in terms of iterations of ${\mathrm{\Pi }}_i$-recursively Mahlo operations for $1\le k\le i<N$.