The minimum-semidegree conjecture for oriented paths

For a digraph $D$, define the semidegree of a vertex by $d^0(v):=\min\{d^-(v),d^+(v)\}$ and the minimum semidegree by $\delta^0(D):=\min\{d^0(v):v\in V(D)\}$. Minimum-semidegree path conjecture. Every oriented graph $D$ with $\delta^0(D)>\frac k2$ contains every oriented path with $k$ edges. The question is presented as a first possible extension of the known spanning-path result; its resolution is not supplied.