#include <bits/stdc++.h>
using namespace std;
void setIO(const string &name) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin.exceptions(istream::failbit);
}
const int inf = 0x3f3f3f3f, mod = 1e9 + 7, maxn = 5e4 + 5, maxk = 505;
vector<int> adj[maxn];
long long dp[maxn][maxk], k;
long long sol = 0;
void dfs(int c, int p) {
  dp[c][0] = 1;
  for (auto &i : adj[c]) {
    if (i != p) {
      dfs(i, c);
      for (int j = 0; j < k; ++j) {
        sol += dp[i][j] * dp[c][k - (j + 1)];
      }
      for (int j = 0; j < k; ++j) {
        dp[c][j + 1] += dp[i][j];
      }
    }
  }
}
int main() {
  setIO("c");
  int n;
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(0, -1);
  cout << sol << "\n";
  return 0;
}

### Prompt

Your task is to create 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;
void setIO(const string &name) {
  ios_base::sync_with_stdio(false);
  cin.tie(nullptr);
  cin.exceptions(istream::failbit);
}
const int inf = 0x3f3f3f3f, mod = 1e9 + 7, maxn = 5e4 + 5, maxk = 505;
vector<int> adj[maxn];
long long dp[maxn][maxk], k;
long long sol = 0;
void dfs(int c, int p) {
  dp[c][0] = 1;
  for (auto &i : adj[c]) {
    if (i != p) {
      dfs(i, c);
      for (int j = 0; j < k; ++j) {
        sol += dp[i][j] * dp[c][k - (j + 1)];
      }
      for (int j = 0; j < k; ++j) {
        dp[c][j + 1] += dp[i][j];
      }
    }
  }
}
int main() {
  setIO("c");
  int n;
  cin >> n >> k;
  for (int i = 0; i < n - 1; ++i) {
    int a, b;
    cin >> a >> b;
    --a, --b;
    adj[a].push_back(b);
    adj[b].push_back(a);
  }
  dfs(0, -1);
  cout << sol << "\n";
  return 0;
}

```