Bulls and Cows

Farmer John wants to arrange $N$ animals ($1 \le N \le 100{,}000$) — bulls and cows — in a single row to present at the annual fair.

FJ has noticed that the bulls have become quite pugnacious lately: if two bulls stand too close together in the line, they will argue and start to fight, ruining the presentation. Being resourceful, FJ has calculated that any two bulls must have at least $K$ cows ($0 \le K < N$) between them in order to avoid a fight.

Help FJ by counting the number of distinct sequences of $N$ bulls and cows that avoid any fighting. All bulls are identical and all cows are identical, so two sequences differ only if some position holds a different kind of animal.

• Line 1: Two space-separated integers, $N$ and $K$.

• Line 1: A single integer — the number of sequences FJ could create. Because this number can be very large, output it modulo $5{,}000{,}011$.

For $N = 4$ and $K = 2$, the six sequences FJ could create are shown below ('C' is a cow and 'B' is a bull):

CCCC
BCCC
CBCC
CCBC
CCCB
BCCB