  Alon and Krivelevich proved that for every $n$-vertex subcubic graph $H$ and
every integer $q \ge 2$ there exists a (smallest) integer $f=f(H,q)$ such that
every $K_f$-minor contains a subdivision of $H$ in which the length of every
subdivision-path is divisible by $q$. Improving their superexponential bound,
we show that $f(H,q) \le \frac{21}{2}qn+8n+14q$, which is optimal up to a
constant multiplicative factor.
