#include <bits/stdc++.h>
using namespace std;
vector<int> a[50002];
int dp[50002][513], n, k, res = 0;
bool fee[50002];
void compute(int u, int v) {
  for (int i = 0; i < k; i++) res += dp[u][i] * dp[v][k - i - 1];
  for (int i = 0; i < k; i++) {
    dp[u][i + 1] += dp[v][i];
  }
}
void dfs(int u) {
  dp[u][0]++;
  fee[u] = false;
  for (auto v : a[u])
    if (fee[v] == true) {
      dfs(v);
      compute(u, v);
    }
}
void debug() {
  for (int u = 1; u <= n; u++) {
    cout << "dinh " << u << endl;
    for (int v = 1; v <= 3; v++) {
      cout << "canh " << v << " " << dp[u][v] << endl;
    }
  }
}
int main() {
  int x, y;
  memset(dp, 0, sizeof(dp)), memset(fee, 1, sizeof(fee));
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    a[x].push_back(y);
    a[y].push_back(x);
  }
  dfs(1);
  cout << res;
}

### Prompt

Please formulate 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;
vector<int> a[50002];
int dp[50002][513], n, k, res = 0;
bool fee[50002];
void compute(int u, int v) {
  for (int i = 0; i < k; i++) res += dp[u][i] * dp[v][k - i - 1];
  for (int i = 0; i < k; i++) {
    dp[u][i + 1] += dp[v][i];
  }
}
void dfs(int u) {
  dp[u][0]++;
  fee[u] = false;
  for (auto v : a[u])
    if (fee[v] == true) {
      dfs(v);
      compute(u, v);
    }
}
void debug() {
  for (int u = 1; u <= n; u++) {
    cout << "dinh " << u << endl;
    for (int v = 1; v <= 3; v++) {
      cout << "canh " << v << " " << dp[u][v] << endl;
    }
  }
}
int main() {
  int x, y;
  memset(dp, 0, sizeof(dp)), memset(fee, 1, sizeof(fee));
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    cin >> x >> y;
    a[x].push_back(y);
    a[y].push_back(x);
  }
  dfs(1);
  cout << res;
}

```