#include <bits/stdc++.h>
using namespace std;
int n, k;
vector<vector<int>> adj;
void input();
long long d[50001][502] = {}, ans[50001], sum = 0;
void dfs(int cur, int prev) {
  d[cur][0] = 1;
  long long sub = 0;
  for (int p : adj[cur])
    if (p != prev) {
      dfs(p, cur);
      for (int i = 1; i <= k; i++) {
        d[cur][i] += d[p][i - 1];
        sub += d[p][i - 1] * d[p][k - 1 - i];
      }
    }
  for (int i = 0; i <= k; i++) ans[cur] += d[cur][i] * d[cur][k - i];
  ans[cur] = (ans[cur] - sub) / 2;
  sum += ans[cur];
}
int main() {
  ios_base::sync_with_stdio(false);
  input();
  dfs(1, 0);
  cout << sum;
}
void input() {
  cin >> n >> k;
  adj.resize(n + 1);
  int x, y;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
}

### 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;
int n, k;
vector<vector<int>> adj;
void input();
long long d[50001][502] = {}, ans[50001], sum = 0;
void dfs(int cur, int prev) {
  d[cur][0] = 1;
  long long sub = 0;
  for (int p : adj[cur])
    if (p != prev) {
      dfs(p, cur);
      for (int i = 1; i <= k; i++) {
        d[cur][i] += d[p][i - 1];
        sub += d[p][i - 1] * d[p][k - 1 - i];
      }
    }
  for (int i = 0; i <= k; i++) ans[cur] += d[cur][i] * d[cur][k - i];
  ans[cur] = (ans[cur] - sub) / 2;
  sum += ans[cur];
}
int main() {
  ios_base::sync_with_stdio(false);
  input();
  dfs(1, 0);
  cout << sum;
}
void input() {
  cin >> n >> k;
  adj.resize(n + 1);
  int x, y;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
}

```