Distinct trees II

Let $T(n,m)$ be the number of distinct trees with $n$ nodes where the distance between any two nodes is no more than $m$. The distance between two vertices $p$ and $q$ is the number of edges we will come across as we travel from vertex $p$ to vertex $q$ in the shortest path. Two trees are not considered distinct if they are isomorphic.

For example, $T(6,3)=3$. Three distinct trees are shown below.

You are given $T(15,4)=128$ and $T(50,7)\equiv 270742753(\mathrm{mod}1000000007)$

Find $T(1000,15)mod1000000007$