#include <bits/stdc++.h>
using namespace std;
int N, K;
vector<int> edge[50000 + 1];
int F[50000 + 1][500 + 1];
long long ans = 0LL;
inline void Tree_DP(const int x, const int fa) {
  F[x][0] = 1;
  for (vector<int>::iterator i = edge[x].begin(); i != edge[x].end(); i++)
    if ((*i) != fa) {
      Tree_DP(*i, x);
      for (int j = 0; j <= K - 1; j++)
        ans += static_cast<long long>(F[x][K - j - 1]) * F[*i][j];
      for (int j = 1; j <= K; j++) F[x][j] += F[*i][j - 1];
    }
}
int main() {
  scanf("%d %d", &N, &K);
  for (int i = 1; i < N; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    edge[a].push_back(b);
    edge[b].push_back(a);
  }
  memset(F, 0, sizeof F);
  Tree_DP(1, 0);
  printf("%I64d\n", ans);
  return 0;
}

### 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;
int N, K;
vector<int> edge[50000 + 1];
int F[50000 + 1][500 + 1];
long long ans = 0LL;
inline void Tree_DP(const int x, const int fa) {
  F[x][0] = 1;
  for (vector<int>::iterator i = edge[x].begin(); i != edge[x].end(); i++)
    if ((*i) != fa) {
      Tree_DP(*i, x);
      for (int j = 0; j <= K - 1; j++)
        ans += static_cast<long long>(F[x][K - j - 1]) * F[*i][j];
      for (int j = 1; j <= K; j++) F[x][j] += F[*i][j - 1];
    }
}
int main() {
  scanf("%d %d", &N, &K);
  for (int i = 1; i < N; i++) {
    int a, b;
    scanf("%d %d", &a, &b);
    edge[a].push_back(b);
    edge[b].push_back(a);
  }
  memset(F, 0, sizeof F);
  Tree_DP(1, 0);
  printf("%I64d\n", ans);
  return 0;
}

```