#include <bits/stdc++.h>
using namespace std;
vector<long long int> adj[200015];
vector<vector<long long int>> dp;
long long int n, ans, k;
void dfs(long long int cur, long long int par) {
  dp[cur][0] = 1;
  for (auto x : adj[cur]) {
    if (x == par) continue;
    dfs(x, cur);
    for (long long int i = 1; i <= k; ++i) dp[cur][i] += dp[x][i - 1];
  }
  long long int c = 0;
  ans += dp[cur][k];
  for (auto x : adj[cur]) {
    if (x == par) continue;
    for (long long int i = 0; i < k - 1; ++i) {
      long long int mi = (dp[cur][k - i - 1] - dp[x][k - i - 2]);
      c += (dp[x][i] * mi);
    }
  }
  ans += c / 2;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  cin >> n >> k;
  dp.resize(n + 1);
  for (long long int i = 1; i <= n; ++i) dp[i].resize(k + 1, 0);
  for (long long int i = 1; i < n; ++i) {
    long long int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(1, -1);
  cout << ans << "\n";
}

### Prompt

In cpp, your task is to solve 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<long long int> adj[200015];
vector<vector<long long int>> dp;
long long int n, ans, k;
void dfs(long long int cur, long long int par) {
  dp[cur][0] = 1;
  for (auto x : adj[cur]) {
    if (x == par) continue;
    dfs(x, cur);
    for (long long int i = 1; i <= k; ++i) dp[cur][i] += dp[x][i - 1];
  }
  long long int c = 0;
  ans += dp[cur][k];
  for (auto x : adj[cur]) {
    if (x == par) continue;
    for (long long int i = 0; i < k - 1; ++i) {
      long long int mi = (dp[cur][k - i - 1] - dp[x][k - i - 2]);
      c += (dp[x][i] * mi);
    }
  }
  ans += c / 2;
}
int main() {
  ios_base::sync_with_stdio(false), cin.tie(NULL);
  cin >> n >> k;
  dp.resize(n + 1);
  for (long long int i = 1; i <= n; ++i) dp[i].resize(k + 1, 0);
  for (long long int i = 1; i < n; ++i) {
    long long int x, y;
    cin >> x >> y;
    adj[x].push_back(y);
    adj[y].push_back(x);
  }
  dfs(1, -1);
  cout << ans << "\n";
}

```