#include <bits/stdc++.h>
using namespace std;
using pii = pair<int, int>;
using ll = long long;
const int maxn = 5e4 + 5;
const int maxk = 505;
const int inf = 1e9;
const int mod = 1e9 + 7;
int n, k;
vector<int> adj[maxn];
int dp[maxn][maxk];
void fill_dp(int u = 1, int p = 1) {
  dp[u][0] = 1;
  for (int v : adj[u])
    if (v != p) {
      fill_dp(v, u);
      for (int i = 1; i <= k; i++) dp[u][i] += dp[v][i - 1];
    }
}
ll solve(int u = 1, int p = 1) {
  ll ans = 2 * dp[u][k];
  for (int i = 1; i <= k - 1; i++)
    for (int v : adj[u])
      if (v != p) ans += dp[v][i - 1] * (dp[u][k - i] - dp[v][k - i - 1]);
  for (int v : adj[u])
    if (v != p) ans += 2 * solve(v, u);
  ans /= 2;
  return ans;
}
int32_t main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n - 1; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    adj[x].emplace_back(y);
    adj[y].emplace_back(x);
  }
  fill_dp();
  printf("%lld\n", solve());
}

### Prompt

Your task is to create 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;
using pii = pair<int, int>;
using ll = long long;
const int maxn = 5e4 + 5;
const int maxk = 505;
const int inf = 1e9;
const int mod = 1e9 + 7;
int n, k;
vector<int> adj[maxn];
int dp[maxn][maxk];
void fill_dp(int u = 1, int p = 1) {
  dp[u][0] = 1;
  for (int v : adj[u])
    if (v != p) {
      fill_dp(v, u);
      for (int i = 1; i <= k; i++) dp[u][i] += dp[v][i - 1];
    }
}
ll solve(int u = 1, int p = 1) {
  ll ans = 2 * dp[u][k];
  for (int i = 1; i <= k - 1; i++)
    for (int v : adj[u])
      if (v != p) ans += dp[v][i - 1] * (dp[u][k - i] - dp[v][k - i - 1]);
  for (int v : adj[u])
    if (v != p) ans += 2 * solve(v, u);
  ans /= 2;
  return ans;
}
int32_t main() {
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n - 1; i++) {
    int x, y;
    scanf("%d %d", &x, &y);
    adj[x].emplace_back(y);
    adj[y].emplace_back(x);
  }
  fill_dp();
  printf("%lld\n", solve());
}

```