I love this puzzle, but I think it's not quite correct: three solutions are compatible with the specifications. Spoilers and discussion in rot13:
Gur svefg naq sbhegu dhrfgvbaf zhfg or nafjrerq "ab", gb nibvq erqhaqnapl, naq gur svsgu zhfg or nafjrerq "lrf" gb trg rabhtu vasbezngvba nobhg gur sbhegu qvtvg, fb jr pna pbafvqre whfg uvagf 2 naq 3.
Gur npprcgrq fbyhgvba pbzrf sebz nafjrevat obgu "lrf". Nafjrevat obgu "ab" qbrfa'g tvir rabhtu vasbezngvba - vg yrnirf, rt, 3419 naq 3149 nf cbffvovyvgvrf. Ohg jr pna nafjre 2 jvgu "lrf" naq 3 jvgu "ab" naq trg n fbyhgvba bs 5219, be nafjre 2 jvgu "ab" naq 3 jvgu "lrf" gb trg n fbyhgvba bs 5039.
Obgu pnfrf yrnir ab erqhaqnag dhrfgvbaf, naq va obgu pnfrf xabjvat gur svir nafjref vf rabhtu gb svaq bar fbyhgvba.