#include <bits/stdc++.h>
using namespace std;
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(false);
  int n, k, a, b;
  cin >> n >> k;
  vector<vector<int> > adj(n);
  for (int i = 1; i < n; ++i) {
    cin >> a >> b;
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  vector<vector<long long int> > d(k + 1, vector<long long int>(n, 1));
  for (int i = 0; i < n; ++i) d[1][i] = adj[i].size();
  for (int i = 1; i < k; ++i) {
    for (int j = 0; j < n; ++j) {
      int t = 0;
      int nadj = adj[j].size();
      for (int l = 0; l < nadj; ++l) t += d[i][adj[j][l]];
      t -= (d[1][j] - 1) * d[i - 1][j];
      if (i == 1) t -= d[0][j];
      d[i + 1][j] = t;
    }
  }
  long long int r = 0;
  for (int i = 0; i < n; ++i) r += d[k][i];
  cout << r / 2 << endl;
  return EXIT_SUCCESS;
}

### Prompt

Please create a solution in cpp to the following problem:

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 "ai bi" (without the quotes) (1 ≤ ai, bi ≤ n, ai ≠ bi), where ai and bi 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).

### Response

```cpp
#include <bits/stdc++.h>
using namespace std;
int main(int argc, char* argv[]) {
  ios_base::sync_with_stdio(false);
  int n, k, a, b;
  cin >> n >> k;
  vector<vector<int> > adj(n);
  for (int i = 1; i < n; ++i) {
    cin >> a >> b;
    a--;
    b--;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  vector<vector<long long int> > d(k + 1, vector<long long int>(n, 1));
  for (int i = 0; i < n; ++i) d[1][i] = adj[i].size();
  for (int i = 1; i < k; ++i) {
    for (int j = 0; j < n; ++j) {
      int t = 0;
      int nadj = adj[j].size();
      for (int l = 0; l < nadj; ++l) t += d[i][adj[j][l]];
      t -= (d[1][j] - 1) * d[i - 1][j];
      if (i == 1) t -= d[0][j];
      d[i + 1][j] = t;
    }
  }
  long long int r = 0;
  for (int i = 0; i < n; ++i) r += d[k][i];
  cout << r / 2 << endl;
  return EXIT_SUCCESS;
}

```