# 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 $k(1≤n≤50000,1≤k≤500)$ — 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 $a_{i}b_{i}(1≤a_{i},b_{i}≤n,a_{i}=b_{i})$, 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 $k$.