IL-GILLIS 2022 Problem 2

Real nonzero numbers $a,b,c,d,e,f,k,m$ satisfy the equations $$\frac{a}{b}+\frac{c}{d}+\frac{e}{f}=k$$ $$\frac{b}{c}+\frac{d}{e}+\frac{f}{a}=m$$ $$ad=be=cf$$ Express $\frac{a}{c}+\frac{c}{e}+\frac{e}{a}+\frac{b}{d}+\frac{d}{f}+\frac{f}{b}$ using $m$ and $k$ .