A tree is a connected graph that doesn't contain any cycles.

The distance between two vertices of a tree is the length (in edges) of the shortest path between these vertices.

You are given a tree with $*n*$ vertices and a positive number $*k*$. Find the number of distinct pairs of the vertices which have a distance of exactly $*k*$ between them. Note that pairs ($*v*$, $*u*$) and ($*u*$, $*v*$) are considered to be the same pair.

Input

The first line contains two integers $*n*$ and $*k*$ ($1 ≤ *n* ≤ 50000$, $1 ≤ *k* ≤ 500$) — the number of vertices and the required distance between the vertices.

Next $*n* - 1$ lines describe the edges as "$*a*_{*i*}$ $*b*_{*i*}$" (without the quotes) ($1 ≤ *a*_{*i*}, *b*_{*i*} ≤ *n*$, $*a*_{*i*} ≠ *b*_{*i*}$), where $*a*_{*i*}$ and $*b*_{*i*}$ are the vertices connected by the $*i*$-th edge. All given edges are different.

Output

Print a single integer — the number of distinct pairs of the tree's vertices which have a distance of exactly $*k*$ between them.

Please do not use the %lld specifier to read or write 64-bit integers in С++. It is preferred to use the cin, cout streams or the %I64d specifier.

Note

In the first sample the pairs of vertexes at distance 2 from each other are (1, 3), (1, 5), (3, 5) and (2, 4).