RU-ALLRUSSIAN 1982 Problem 6

ABCD is a parallelogram and AB is not equal to BC. M is chosen so that (1) $\angle \mathrm{MAC} =$ $\angle \mathrm{DAC}$ and M is on the opposite side of AC to D, and (2) $\angle \mathrm{MBD} = \angle \mathrm{CBD}$ and M is on the opposite side of BD to C. Find AM/BM in terms of $\mathrm{k} = \mathrm{AC} / \mathrm{BD}$ .