#include <bits/stdc++.h>
using namespace std;
bool* taken;
vector<int>* g;
int* depth;
int* subtree;
int n;
void dfs_depth(int node, int p) {
  subtree[node] = 1;
  depth[node] = 1;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    dfs_depth(u, node);
    depth[node] = max(depth[node], depth[u]);
    subtree[node] += subtree[u];
  }
}
int dfsCent(int node, int p, int pr) {
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    if (subtree[u] * 2 > (subtree[node] + pr))
      return dfsCent(u, node, subtree[node] - subtree[u] + pr);
  }
  return node;
}
int centroid_(int node) {
  dfs_depth(node, -1);
  return dfsCent(node, -1, 0);
}
long long int ans = 0;
int sum = 0;
long long int* vals;
long long int* temp;
int k;
void dfs(int node, int d, int p) {
  if (d > k) return;
  ans += vals[k - d];
  temp[d]++;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    dfs(u, d + 1, node);
  }
}
void solve(int node) {
  int MXX = k + 2;
  vals = new long long int[MXX];
  temp = new long long int[MXX];
  for (int i = 0; i < MXX; i++) vals[i] = 0;
  vals[0] = 1;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (taken[u]) continue;
    for (int j = 0; j < MXX; j++) temp[j] = 0;
    dfs(u, 1, node);
    for (int j = 0; j < MXX; j++) vals[j] += temp[j];
  }
  taken[node] = 1;
}
int main() {
  cin >> n >> k;
  g = new vector<int>[n];
  subtree = new int[n];
  depth = new int[n];
  taken = new bool[n];
  for (int i = 0; i < n; i++) subtree[i] = depth[i] = taken[i] = 0;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  for (int i = 0; i < n; i++) {
    if (taken[i]) continue;
    int cen = centroid_(i);
    solve(cen);
    i--;
  }
  cout << ans << endl;
  return 0;
}

### Prompt

Please create a solution in cpp 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;
bool* taken;
vector<int>* g;
int* depth;
int* subtree;
int n;
void dfs_depth(int node, int p) {
  subtree[node] = 1;
  depth[node] = 1;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    dfs_depth(u, node);
    depth[node] = max(depth[node], depth[u]);
    subtree[node] += subtree[u];
  }
}
int dfsCent(int node, int p, int pr) {
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    if (subtree[u] * 2 > (subtree[node] + pr))
      return dfsCent(u, node, subtree[node] - subtree[u] + pr);
  }
  return node;
}
int centroid_(int node) {
  dfs_depth(node, -1);
  return dfsCent(node, -1, 0);
}
long long int ans = 0;
int sum = 0;
long long int* vals;
long long int* temp;
int k;
void dfs(int node, int d, int p) {
  if (d > k) return;
  ans += vals[k - d];
  temp[d]++;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (u == p || taken[u]) continue;
    dfs(u, d + 1, node);
  }
}
void solve(int node) {
  int MXX = k + 2;
  vals = new long long int[MXX];
  temp = new long long int[MXX];
  for (int i = 0; i < MXX; i++) vals[i] = 0;
  vals[0] = 1;
  for (int i = 0; i < g[node].size(); i++) {
    int u = g[node][i];
    if (taken[u]) continue;
    for (int j = 0; j < MXX; j++) temp[j] = 0;
    dfs(u, 1, node);
    for (int j = 0; j < MXX; j++) vals[j] += temp[j];
  }
  taken[node] = 1;
}
int main() {
  cin >> n >> k;
  g = new vector<int>[n];
  subtree = new int[n];
  depth = new int[n];
  taken = new bool[n];
  for (int i = 0; i < n; i++) subtree[i] = depth[i] = taken[i] = 0;
  for (int i = 0; i < n - 1; i++) {
    int a, b;
    cin >> a >> b;
    a--;
    b--;
    g[a].push_back(b);
    g[b].push_back(a);
  }
  for (int i = 0; i < n; i++) {
    if (taken[i]) continue;
    int cen = centroid_(i);
    solve(cen);
    i--;
  }
  cout << ans << endl;
  return 0;
}

```