#include <bits/stdc++.h>
using namespace std;
const double EPS = 1e-9;
const long long INF = 1000000000000000000;
const int intINF = 2000000000;
const int maxn = 50005;
long long ANS;
vector<int> e[maxn];
int K;
vector<int> dfs(int v, int f = -1) {
  vector<int> s(K + 1, 0);
  vector<vector<int> > b(e[v].size());
  for (int _n(e[v].size()), i(0); i < _n; i++)
    if (e[v][i] != f) {
      b[i] = dfs(e[v][i], v);
      for (int j = K; j > 0; --j) b[i][j] = b[i][j - 1];
      b[i][0] = 0;
      for (int _n(K + 1), j(0); j < _n; j++) s[j] += b[i][j];
    }
  vector<int> ret = s;
  for (int _n(e[v].size()), i(0); i < _n; i++)
    if (e[v][i] != f) {
      vector<int> &cur = b[i];
      long long t = 0;
      for (int _n(K), j(1); j < _n; j++)
        t += (long long)(s[j] - cur[j]) * (cur[K - j]);
      for (int _n(K + 1), j(0); j < _n; j++) s[j] -= cur[j];
      ANS += t;
    }
  ANS += ret[K];
  ret[0] = 1;
  return ret;
}
int main() {
  int N;
  cin >> N >> K;
  for (int _n(N - 1), i(0); i < _n; i++) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    e[a].push_back(b);
    e[b].push_back(a);
  }
  ANS = 0;
  dfs(0);
  cout << ANS << endl;
}

### Prompt

Your challenge is to write a CPP solution 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;
const double EPS = 1e-9;
const long long INF = 1000000000000000000;
const int intINF = 2000000000;
const int maxn = 50005;
long long ANS;
vector<int> e[maxn];
int K;
vector<int> dfs(int v, int f = -1) {
  vector<int> s(K + 1, 0);
  vector<vector<int> > b(e[v].size());
  for (int _n(e[v].size()), i(0); i < _n; i++)
    if (e[v][i] != f) {
      b[i] = dfs(e[v][i], v);
      for (int j = K; j > 0; --j) b[i][j] = b[i][j - 1];
      b[i][0] = 0;
      for (int _n(K + 1), j(0); j < _n; j++) s[j] += b[i][j];
    }
  vector<int> ret = s;
  for (int _n(e[v].size()), i(0); i < _n; i++)
    if (e[v][i] != f) {
      vector<int> &cur = b[i];
      long long t = 0;
      for (int _n(K), j(1); j < _n; j++)
        t += (long long)(s[j] - cur[j]) * (cur[K - j]);
      for (int _n(K + 1), j(0); j < _n; j++) s[j] -= cur[j];
      ANS += t;
    }
  ANS += ret[K];
  ret[0] = 1;
  return ret;
}
int main() {
  int N;
  cin >> N >> K;
  for (int _n(N - 1), i(0); i < _n; i++) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    e[a].push_back(b);
    e[b].push_back(a);
  }
  ANS = 0;
  dfs(0);
  cout << ANS << endl;
}

```