#include <bits/stdc++.h>
using namespace std;
const int MAX = 50050;
vector<int> e[MAX];
vector<int> ee[MAX];
int c[MAX][555];
int vis[MAX];
int n, k;
void solve(int indx) {
  c[indx][0] = 1;
  vis[indx] = 1;
  for (int i = 0; i < e[indx].size(); i++) {
    if (vis[e[indx][i]] == 1) continue;
    int cindx = e[indx][i];
    ee[indx].push_back(cindx);
    solve(cindx);
    for (int j = 0; j <= k; j++) {
      if (c[cindx][j] == 0) break;
      c[indx][j + 1] += c[cindx][j];
    }
  }
}
long long solve1() {
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long ret = 0;
    for (int j = 0; j < ee[i].size(); j++) {
      for (int K = 1; K < k; K++) {
        long long first = 0, second = 0;
        first = c[ee[i][j]][K - 1];
        second = c[i][k - K] - c[ee[i][j]][k - K - 1];
        ret += (first * second);
      }
    }
    ans += ret / 2;
    ans += c[i][k];
  }
  return ans;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    e[x].push_back(y);
    e[y].push_back(x);
  }
  solve(1);
  cout << solve1() << endl;
}

### Prompt

Create a solution in Cpp for 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 MAX = 50050;
vector<int> e[MAX];
vector<int> ee[MAX];
int c[MAX][555];
int vis[MAX];
int n, k;
void solve(int indx) {
  c[indx][0] = 1;
  vis[indx] = 1;
  for (int i = 0; i < e[indx].size(); i++) {
    if (vis[e[indx][i]] == 1) continue;
    int cindx = e[indx][i];
    ee[indx].push_back(cindx);
    solve(cindx);
    for (int j = 0; j <= k; j++) {
      if (c[cindx][j] == 0) break;
      c[indx][j + 1] += c[cindx][j];
    }
  }
}
long long solve1() {
  long long ans = 0;
  for (int i = 1; i <= n; i++) {
    long long ret = 0;
    for (int j = 0; j < ee[i].size(); j++) {
      for (int K = 1; K < k; K++) {
        long long first = 0, second = 0;
        first = c[ee[i][j]][K - 1];
        second = c[i][k - K] - c[ee[i][j]][k - K - 1];
        ret += (first * second);
      }
    }
    ans += ret / 2;
    ans += c[i][k];
  }
  return ans;
}
int main() {
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int x, y;
    cin >> x >> y;
    e[x].push_back(y);
    e[y].push_back(x);
  }
  solve(1);
  cout << solve1() << endl;
}

```