A minimal pair of $K$-degrees

We construct a minimal pair of $K$-degrees. We do this by showing the existence of an unbounded nondecreasing function $f$ which forces $K$-triviality in the sense that $\gamma\in 2^\omega$ is $K$-trivial if and only if for all $n$, $K(\gamma\upharpoonright n) \leq K(n) + f(n)+ \mathcal{O}(1)$.