MONI can find k-MEMs

Maximal exact matches (MEMs) have been widely used in bioinformatics at least since Li (2013) presented BWA-MEM. Building on work by Bannai, Gagie and I (2018), Rossi et al.\ (2022) recently built an index called MONI, based on the run-length compressed Burrows-Wheeler Transform, that can find MEMs efficiently with respect to pangenomes. In this paper we define $k$-MEMs to be maximal substrings of a pattern that each occur exactly at $k$ times in a text (so a MEM is a 1-MEM) and show that, when $k$ is given at construction time, MONI can find $k$-MEMs efficiently as well.