The package for this problem was not updated by the problem writer or Codeforces administration after we've upgraded the judging servers. To adjust the time limit constraint, a solution execution time will be multiplied by 2. For example, if your solution works for 400 ms on judging servers, then the value 800 ms will be displayed and used to determine the verdict.

VK Cup 2012 Round 1 |
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Finished |

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dp

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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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