#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1000000007;
const long long INF = 1000000000;
template <class T>
inline void read(T &x) {
  char c;
  int flag = 1;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') flag *= -1;
  x = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') x = x * 10 + c - '0';
  x *= flag;
  return;
}
int dp[50005][505];
vector<int> adj[50005];
int ans = 0;
int n, k;
inline void dfs(int x, int fa) {
  for (auto i : adj[x]) {
    if (i == fa) continue;
    dfs(i, x);
    for (int j = 1; j <= k; ++j) {
      ans += dp[x][(k)-j] * dp[i][j - 1];
    }
    for (int j = 1; j <= k; ++j) dp[x][j] += dp[i][j - 1];
  }
  ans += dp[x][k];
  dp[x][0]++;
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(1, -1);
  cout << (ans) << 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 long long MOD = 1000000007;
const long long INF = 1000000000;
template <class T>
inline void read(T &x) {
  char c;
  int flag = 1;
  while ((c = getchar()) < '0' || c > '9')
    if (c == '-') flag *= -1;
  x = c - '0';
  while ((c = getchar()) >= '0' && c <= '9') x = x * 10 + c - '0';
  x *= flag;
  return;
}
int dp[50005][505];
vector<int> adj[50005];
int ans = 0;
int n, k;
inline void dfs(int x, int fa) {
  for (auto i : adj[x]) {
    if (i == fa) continue;
    dfs(i, x);
    for (int j = 1; j <= k; ++j) {
      ans += dp[x][(k)-j] * dp[i][j - 1];
    }
    for (int j = 1; j <= k; ++j) dp[x][j] += dp[i][j - 1];
  }
  ans += dp[x][k];
  dp[x][0]++;
  return;
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(1, -1);
  cout << (ans) << endl;
}

```