#include <bits/stdc++.h>
using namespace std;
const int MAXN = 50007, INF = 1e9 + 7;
int n, sz[MAXN], k, total = 0, dad[MAXN], pa[20][MAXN], h[MAXN] = {};
set<int> adj[MAXN];
vector<int> nxt[MAXN];
map<int, int> cnt[MAXN];
long long res = 0;
vector<pair<int, int> > save;
void dfs_subtree(int u, int p) {
  sz[u] = 1, ++total;
  for (auto v : adj[u])
    if (v != p) dfs_subtree(v, u), sz[u] += sz[v];
}
int findCentroid(int u, int p) {
  for (auto v : adj[u])
    if (v != p && sz[v] > total / 2) return findCentroid(v, u);
  return u;
}
void centroidDecomp(int u, int p) {
  total = 0;
  dfs_subtree(u, u);
  int centroid = findCentroid(u, u);
  dad[centroid] = p, nxt[p].push_back(centroid);
  for (auto v : adj[centroid])
    adj[v].erase(centroid), centroidDecomp(v, centroid);
  adj[centroid].clear();
}
void dfs_lca(int u, int p) {
  for (auto v : adj[u])
    if (v != p) pa[0][v] = u, h[v] = h[u] + 1, dfs_lca(v, u);
}
void build_lca() {
  for (int i = 1; i < 20; ++i)
    for (int u = 1; u <= n; ++u) pa[i][u] = pa[i - 1][pa[i - 1][u]];
}
int dist(int u, int v) {
  int res = 0;
  if (h[u] < h[v]) swap(u, v);
  for (int i = 19; i >= 0; --i)
    if (h[u] - (1 << i) >= h[v]) u = pa[i][u], res += (1 << i);
  if (u == v) return res;
  for (int i = 19; i >= 0; --i)
    if (pa[i][u] != pa[i][v]) res += (1 << (i + 1)), v = pa[i][v], u = pa[i][u];
  return res + 2;
}
void calc(int u, int s) {
  int d = dist(s, u);
  if (k >= d) res += 1LL * cnt[s][k - d];
  for (auto v : nxt[u]) calc(v, s);
}
void upd(int u, int s) {
  int d = dist(s, u);
  ++cnt[s][d];
  for (auto v : nxt[u]) upd(v, s);
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int u, v;
    cin >> u >> v;
    adj[u].insert(v), adj[v].insert(u);
  }
  dfs_lca(1, 0);
  build_lca();
  centroidDecomp(1, 0);
  for (int i = 1; i <= n; ++cnt[i][0], ++i)
    ;
  for (int i = 1; i <= n; ++i)
    for (auto v : nxt[i]) calc(v, i), upd(v, i);
  cout << res;
  return 0;
}

### Prompt

Your challenge is to write 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;
const int MAXN = 50007, INF = 1e9 + 7;
int n, sz[MAXN], k, total = 0, dad[MAXN], pa[20][MAXN], h[MAXN] = {};
set<int> adj[MAXN];
vector<int> nxt[MAXN];
map<int, int> cnt[MAXN];
long long res = 0;
vector<pair<int, int> > save;
void dfs_subtree(int u, int p) {
  sz[u] = 1, ++total;
  for (auto v : adj[u])
    if (v != p) dfs_subtree(v, u), sz[u] += sz[v];
}
int findCentroid(int u, int p) {
  for (auto v : adj[u])
    if (v != p && sz[v] > total / 2) return findCentroid(v, u);
  return u;
}
void centroidDecomp(int u, int p) {
  total = 0;
  dfs_subtree(u, u);
  int centroid = findCentroid(u, u);
  dad[centroid] = p, nxt[p].push_back(centroid);
  for (auto v : adj[centroid])
    adj[v].erase(centroid), centroidDecomp(v, centroid);
  adj[centroid].clear();
}
void dfs_lca(int u, int p) {
  for (auto v : adj[u])
    if (v != p) pa[0][v] = u, h[v] = h[u] + 1, dfs_lca(v, u);
}
void build_lca() {
  for (int i = 1; i < 20; ++i)
    for (int u = 1; u <= n; ++u) pa[i][u] = pa[i - 1][pa[i - 1][u]];
}
int dist(int u, int v) {
  int res = 0;
  if (h[u] < h[v]) swap(u, v);
  for (int i = 19; i >= 0; --i)
    if (h[u] - (1 << i) >= h[v]) u = pa[i][u], res += (1 << i);
  if (u == v) return res;
  for (int i = 19; i >= 0; --i)
    if (pa[i][u] != pa[i][v]) res += (1 << (i + 1)), v = pa[i][v], u = pa[i][u];
  return res + 2;
}
void calc(int u, int s) {
  int d = dist(s, u);
  if (k >= d) res += 1LL * cnt[s][k - d];
  for (auto v : nxt[u]) calc(v, s);
}
void upd(int u, int s) {
  int d = dist(s, u);
  ++cnt[s][d];
  for (auto v : nxt[u]) upd(v, s);
}
int main() {
  ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i < n; ++i) {
    int u, v;
    cin >> u >> v;
    adj[u].insert(v), adj[v].insert(u);
  }
  dfs_lca(1, 0);
  build_lca();
  centroidDecomp(1, 0);
  for (int i = 1; i <= n; ++cnt[i][0], ++i)
    ;
  for (int i = 1; i <= n; ++i)
    for (auto v : nxt[i]) calc(v, i), upd(v, i);
  cout << res;
  return 0;
}

```