#include <bits/stdc++.h>
using namespace std;
long long br, k;
vector<long long> tree[50005];
long long dp[50005][505];
long long par[50005];
void calcdp(long long vertex, long long parent) {
  dp[vertex][0] = 1;
  par[vertex] = parent;
  for (long long att : tree[vertex]) {
    if (att == parent) continue;
    calcdp(att, vertex);
    for (long long i = 1; i <= k; ++i) {
      dp[vertex][i] += dp[att][i - 1];
    }
  }
}
int main() {
  cin >> br >> k;
  for (long long i = 0; i < br - 1; ++i) {
    long long from, to;
    cin >> from >> to;
    tree[from].push_back(to);
    tree[to].push_back(from);
  }
  calcdp(1, -1);
  long long result = 0;
  for (long long i = 1; i <= br; ++i) {
    result += dp[i][k];
    long long teksum = 0;
    for (long long att : tree[i]) {
      if (att == par[i]) continue;
      for (long long p = 0; p <= k - 2; ++p) {
        long long current =
            dp[att][p] * (dp[i][k - p - 1] - dp[att][k - p - 2]);
        teksum += current;
      }
    }
    teksum /= 2;
    result += teksum;
  }
  cout << result << '\n';
  return 0;
}

### Prompt

Please create a solution in Cpp 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 br, k;
vector<long long> tree[50005];
long long dp[50005][505];
long long par[50005];
void calcdp(long long vertex, long long parent) {
  dp[vertex][0] = 1;
  par[vertex] = parent;
  for (long long att : tree[vertex]) {
    if (att == parent) continue;
    calcdp(att, vertex);
    for (long long i = 1; i <= k; ++i) {
      dp[vertex][i] += dp[att][i - 1];
    }
  }
}
int main() {
  cin >> br >> k;
  for (long long i = 0; i < br - 1; ++i) {
    long long from, to;
    cin >> from >> to;
    tree[from].push_back(to);
    tree[to].push_back(from);
  }
  calcdp(1, -1);
  long long result = 0;
  for (long long i = 1; i <= br; ++i) {
    result += dp[i][k];
    long long teksum = 0;
    for (long long att : tree[i]) {
      if (att == par[i]) continue;
      for (long long p = 0; p <= k - 2; ++p) {
        long long current =
            dp[att][p] * (dp[i][k - p - 1] - dp[att][k - p - 2]);
        teksum += current;
      }
    }
    teksum /= 2;
    result += teksum;
  }
  cout << result << '\n';
  return 0;
}

```