Malkoff modules: M31xx are brighter with shorter runtime. I would not consider full M31 on 1x123, you will get only 40 minutes of runtime based on tests. I would seriously consider either M31L or M31LL to push your runtime into hours and not minutes.
IMO, M31 really shines on 2xAA cells.
Also seriously consider M61LL that will also run very nicely on 1x123 with about a 10-15 hour runtime, mostly circa 30-40 lumens I think, if that's sufficient for you. It starts pretty bright at 50-80 lumens but drops after 30 minutes to half that and the rest of the very long runtime runs out of regulation.
M61LL in 3P is the ultimate EDC lite. It's also the most diverse module Malkoff has, you can stick it anywhere - 3P, 6P, 9P, 12P assuming 2x18650 config.... including 2xAA or 3xAA configurations. The lumens will vary of course based on input.