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.
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 ai bi (1≤ai,bi≤n,ai=bi), where ai and bi are the vertices of the tree connected by the i-th edge. All specified edges are different.
Print a single integer — the number of distinct pairs of tree vertices whose distance is equal to k.