A connected graph without cycles is called a tree. The distance between two vertices of a tree is defined as the length (in edges) of the shortest path between these vertices. Given a tree with $n$ vertices and a positive integer $k$. Compute the number of distinct pairs of vertices of the tree whose distance is equal to $k$. Note that pairs $(v, u)$ and $(u, v)$ are considered the same pair. \InputFile The first line contains two integers $n$ and $k~(1 \le n \le 50000, 1 \le k \le 500)$ --- the number of vertices in the tree and the required distance between vertices. The next $n - 1$ lines contain the edges of the tree in the format $a_i~b_i~(1 \le a_i, b_i \le n, a_i \neq b_i)$, where $a_i$ and $b_i$ are the vertices of the tree connected by the $i$-th edge. All specified edges are different. \OutputFile Print a single integer --- the number of distinct pairs of tree vertices whose distance is equal to $k$. \includegraphics{https://static.e-olymp.com/content/cb/cbaa734ea6b17dc4868689a194b170b734ea3888.gif}