#include <bits/stdc++.h>
using namespace std;
const int inf = 1e9 + 5;
template <class T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
const int MAXN = 5e4 + 5;
const int MAXK = 510;
vector<int> way[MAXN];
int N, K;
long long ans;
vector<long long> f(int node, int pre) {
  vector<long long> res(MAXK, 0);
  res[0] = 1LL;
  for (int(i) = (0); (i) < (way[node].size()); (i)++)
    if (way[node][i] != pre) {
      vector<long long> v = f(way[node][i], node);
      vector<long long> eski = res;
      for (int(j) = (0); (j) < (K); (j)++) {
        if (j + 1 <= K) ans += eski[K - (j + 1)] * v[j];
        if (j + 1 < MAXK) res[j + 1] += v[j];
      }
    }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> N >> K;
  for (int(i) = (1); (i) <= (N - 1); (i)++) {
    int a, b;
    cin >> a >> b;
    way[a].push_back(b);
    way[b].push_back(a);
  }
  f(1, -1);
  cout << ans << endl;
  return 0;
}

### Prompt

Your challenge is to write 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 int inf = 1e9 + 5;
template <class T>
inline T abs(T a) {
  return a > 0 ? a : -a;
}
const int MAXN = 5e4 + 5;
const int MAXK = 510;
vector<int> way[MAXN];
int N, K;
long long ans;
vector<long long> f(int node, int pre) {
  vector<long long> res(MAXK, 0);
  res[0] = 1LL;
  for (int(i) = (0); (i) < (way[node].size()); (i)++)
    if (way[node][i] != pre) {
      vector<long long> v = f(way[node][i], node);
      vector<long long> eski = res;
      for (int(j) = (0); (j) < (K); (j)++) {
        if (j + 1 <= K) ans += eski[K - (j + 1)] * v[j];
        if (j + 1 < MAXK) res[j + 1] += v[j];
      }
    }
  return res;
}
int main() {
  ios_base::sync_with_stdio(false);
  cin >> N >> K;
  for (int(i) = (1); (i) <= (N - 1); (i)++) {
    int a, b;
    cin >> a >> b;
    way[a].push_back(b);
    way[b].push_back(a);
  }
  f(1, -1);
  cout << ans << endl;
  return 0;
}

```