Distance in Tree

Description:

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.

Sample Input:

5 2
1 2
2 3
3 4
2 5

Sample Output:

4

Sample Input:

5 3
1 2
2 3
3 4
4 5

Sample Output:

2

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).