IMO 1984 - Shortlisted Problems Question 16

(POL 1) IMO6 Let $a,b,c,d$ be odd positive integers such that $a\lt b\lt c\lt d$, $ad=bc$, and $a+d=2^k$, $b+c=2^m$ for some integers $k$ and $m$. Prove that $a=1$.