There are $n+1$ stones in a pond, numbered $0$ to $n$.

A frog starts by jumping onto stone $0$. It then jumps between the stones, only ever jumping to adjacent ones. For fixed $k$, it makes exactly $k+i$ visits to each stone $i$ for $0\le i<n$; however, there are no restrictions on the number of times stone $n$ is visited. The frog can finish on any stone.

If $n=3$ and $k=2$ it would visit stone $0$ two times, stone $1$ three times and stone $2$ four times.
One way of achieving this is:
$0\to 1\to 0\to 1\to 2\to 3\to 2\to 1\to 2\to 3\to 2$.

Let $J(n,k)$ be the number of ways the frog can make such a journey. For example, $J(3,2)=17$, $J(6,1)=1320$ and $J(6,5)=16793280$.

Find ${\displaystyle \sum _{s=0}^{4}J(500,{10}^s)}$. Give your answer modulo $987898789$.