P2767 Number of Trees

Compute the number of rooted $m$-ary trees (unlabeled) with $n$ nodes, modulo $10\,007$. Two rooted trees are identical if and only if their roots are identical and, from left to right, each subtree is also identical. In particular, if both rooted trees are empty, they are considered identical.

Input two integers $n$, $m$.

Output the number of rooted $m$-ary trees (unlabeled) with $n$ nodes, modulo $10\,007$.

Constraints: $n, m \leq 127$. Translated by ChatGPT 5