Consider a game in the integer points of the real line, where an Angel tries to escape from a Devil. A positive integer $k$ is chosen, and the Angel and the Devil take turns playing. Initially, no point is blocked. The Angel, in point $A$, can move to any point $P$ such that $|AP| \le k$, as long as $P$ is not blocked. The Devil may block an arbitrary point. The Angel loses if it cannot move and wins if it does not lose in finitely many turns. Let $f(k)$ denote the least number of rounds the Devil takes to win. Prove that $$0.5 k \log_2 (k) (1 + o(1)) \le f(k) \le k \log_2(k) (1 +o(1)).$$ Note: $a(x) = b(x) (1+o(1))$ if $\lim_{x \to \infty} \frac{b(x)}{a(x)} = 1$.