Fixed-Length Paths I

Given a tree of n nodes, your task is to count the number of distinct paths that consist of exactly k edges.

Input

The first input line contains two integers n and k: the number of nodes and the path length. The nodes are numbered 1,2,\ldots,n. Then there are n-1 lines describing the edges. Each line contains two integers a and b: there is an edge between nodes a and b.

Output

Print one integer: the number of paths.

Constraints

$1 \le k \le n \le 2 \cdot 10^5$

$1 \le a,b \le n$

Example

Input

5 2
1 2
2 3
3 4
3 5

Output

4