Dancing in Circles

A kindergarten is attended by $n$ children. Every day the children arrange themselves into $k$ circles and dance. Each circle must contain at least $l$ children.

Two arrangements are considered different if some child has a different right-hand neighbour in one arrangement than in the other. In other words, each circle is a directed ring in which every child has exactly one right neighbour, and the circles themselves are unordered.

Compute the number of distinct arrangements modulo $2005$. If no arrangement satisfies these conditions, the answer is $0$.

The first and only line contains three integers separated by single spaces: $n$, $k$, and $l$.

• $n$: the number of children ($3 \le n \le 10^9$)
• $k$: the number of circles ($1 \le k \le n$)
• $l$: the minimum number of children in each circle ($2 \le l \le n$)

Print, on a single line, the number of distinct arrangements modulo $2005$.