#include <bits/stdc++.h>
using namespace std;
long long res = 0;
int n, k;
vector<int> g[101000];
int ret[51000][505];
void rec(int u, int p) {
  for (int v = 0; v < g[u].size(); ++v) {
    int to = g[u][v];
    if (to == p) continue;
    rec(to, u);
    for (int i = 0; i <= k - 2; ++i) {
      res += ret[u][i] * ret[to][k - i - 2];
    }
    for (int i = 0; i <= k; ++i) {
      ret[u][i] += ret[to][i];
    }
  }
  for (int i = k; i > 0; --i) {
    ret[u][i] = ret[u][i - 1];
  }
  ret[u][0] = 1;
  res += ret[u][k];
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  rec(0, -1);
  if (k == 0)
    cout << 0 << endl;
  else
    cout << res << endl;
  return 0;
}

### Prompt

Generate 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;
long long res = 0;
int n, k;
vector<int> g[101000];
int ret[51000][505];
void rec(int u, int p) {
  for (int v = 0; v < g[u].size(); ++v) {
    int to = g[u][v];
    if (to == p) continue;
    rec(to, u);
    for (int i = 0; i <= k - 2; ++i) {
      res += ret[u][i] * ret[to][k - i - 2];
    }
    for (int i = 0; i <= k; ++i) {
      ret[u][i] += ret[to][i];
    }
  }
  for (int i = k; i > 0; --i) {
    ret[u][i] = ret[u][i - 1];
  }
  ret[u][0] = 1;
  res += ret[u][k];
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int u, v;
    cin >> u >> v;
    --u;
    --v;
    g[u].push_back(v);
    g[v].push_back(u);
  }
  rec(0, -1);
  if (k == 0)
    cout << 0 << endl;
  else
    cout << res << endl;
  return 0;
}

```