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D. Distance in Tree

time limit per test

3 secondsmemory limit per test

512 megabytesinput

standard inputoutput

standard outputA 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.

Examples

Input

5 2

1 2

2 3

3 4

2 5

Output

4

Input

5 3

1 2

2 3

3 4

4 5

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).

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