Distance in Tree

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.

Input

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 $a_i{b}_i(1\le a_i,b_i\le n,a_i\ne b_i)$, where $a_i$ and $b_i$ are the vertices of the tree connected by the $i$-th edge. All specified edges are different.

Output

Print a single integer — the number of distinct pairs of tree vertices whose distance is equal to $k$.

Examples