#include <bits/stdc++.h>
using namespace std;
vector<int> grafo[100100];
bool flag[100100] = {false};
long long ans;
int n, k;
vector<long long> DFS(int x) {
  flag[x] = true;
  vector<long long> v(k + 5);
  v[0] = 1;
  for (int i = 0; i < grafo[x].size(); i++) {
    int y = grafo[x][i];
    if (flag[y]) continue;
    vector<long long> aux = DFS(y);
    for (int j = 0; j < k; j++) {
      ans += v[j] * aux[k - j - 1];
    }
    for (int j = 1; j < k; j++) {
      v[j] += aux[j - 1];
    }
  }
  return v;
}
int main() {
  ans = 0;
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    grafo[x].push_back(y);
    grafo[y].push_back(x);
  }
  DFS(1);
  cout << ans << endl;
}

### 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;
vector<int> grafo[100100];
bool flag[100100] = {false};
long long ans;
int n, k;
vector<long long> DFS(int x) {
  flag[x] = true;
  vector<long long> v(k + 5);
  v[0] = 1;
  for (int i = 0; i < grafo[x].size(); i++) {
    int y = grafo[x][i];
    if (flag[y]) continue;
    vector<long long> aux = DFS(y);
    for (int j = 0; j < k; j++) {
      ans += v[j] * aux[k - j - 1];
    }
    for (int j = 1; j < k; j++) {
      v[j] += aux[j - 1];
    }
  }
  return v;
}
int main() {
  ans = 0;
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    grafo[x].push_back(y);
    grafo[y].push_back(x);
  }
  DFS(1);
  cout << ans << endl;
}

```