#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000000 + 7;
const int max_n = 50001, max_k = 501;
int n, k;
vector<int> *v;
int dp[max_n][max_k];
int ans = 0;
void dfs(int s, int p) {
  dp[s][0] = 1;
  for (int d : v[s]) {
    if (d != p) {
      dfs(d, s);
      for (int i = 0; i < k; i++) ans += (dp[d][i] * dp[s][k - i - 1]);
      for (int i = 0; i < k; i++) dp[s][i + 1] += dp[d][i];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  v = new vector<int>[n + 1];
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  dfs(1, -1);
  cout << ans << 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;
const long long MOD = 1000000000 + 7;
const int max_n = 50001, max_k = 501;
int n, k;
vector<int> *v;
int dp[max_n][max_k];
int ans = 0;
void dfs(int s, int p) {
  dp[s][0] = 1;
  for (int d : v[s]) {
    if (d != p) {
      dfs(d, s);
      for (int i = 0; i < k; i++) ans += (dp[d][i] * dp[s][k - i - 1]);
      for (int i = 0; i < k; i++) dp[s][i + 1] += dp[d][i];
    }
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  v = new vector<int>[n + 1];
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  dfs(1, -1);
  cout << ans << endl;
  return 0;
}

```