= Solution
For $k=0$, the target is reached at time zero, so $h_0=1$. For $k<0$, the preceding <almost sure convergence> gives $Y_n\to+\infty$ with <probability> one. A <sample path> with unit upward and downward steps must visit every intermediate <integer> when it crosses from a negative value to a positive value. It must therefore visit zero at a finite time. Thus
$$
\boxed{h_k=1\quad\text{for every }k\leq0.}
$$
The unit-step property matters: positive long-run displacement alone would not force a walk with larger upward jumps to land exactly on zero.
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