#include <bits/stdc++.h>
using namespace std;
const int MAXN = 5e4 + 10;
const int MAXK = 5e2 + 10;
template <typename T>
void print(const T& a, string end = "\n") {
  cout << a << end;
}
int dist[MAXN][MAXK];
int n, k;
vector<int> G[MAXN];
long long ans = 0;
void solve(int x, int p) {
  dist[x][0] = 1;
  for (int u : G[x]) {
    if (u == p) continue;
    solve(u, x);
    for (int d = 0; d < k; d++) {
      dist[x][d + 1] += dist[u][d];
    }
  }
  for (int u : G[x]) {
    if (u == p) continue;
    for (int d = 1; d < k; d++) {
      ans += (dist[x][k - d] - dist[u][k - d - 1]) * dist[u][d - 1];
    }
  }
}
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  solve(1, 0);
  ans /= 2ll;
  for (int i = 1; i <= n; i++) ans += dist[i][k];
  cout << ans << "\n";
}

### Prompt

Develop a solution in CPP to the problem described below:

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 MAXN = 5e4 + 10;
const int MAXK = 5e2 + 10;
template <typename T>
void print(const T& a, string end = "\n") {
  cout << a << end;
}
int dist[MAXN][MAXK];
int n, k;
vector<int> G[MAXN];
long long ans = 0;
void solve(int x, int p) {
  dist[x][0] = 1;
  for (int u : G[x]) {
    if (u == p) continue;
    solve(u, x);
    for (int d = 0; d < k; d++) {
      dist[x][d + 1] += dist[u][d];
    }
  }
  for (int u : G[x]) {
    if (u == p) continue;
    for (int d = 1; d < k; d++) {
      ans += (dist[x][k - d] - dist[u][k - d - 1]) * dist[u][d - 1];
    }
  }
}
int main() {
  ios::sync_with_stdio(false), cin.tie(nullptr);
  cin >> n >> k;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    G[a].push_back(b);
    G[b].push_back(a);
  }
  solve(1, 0);
  ans /= 2ll;
  for (int i = 1; i <= n; i++) ans += dist[i][k];
  cout << ans << "\n";
}

```