#include <bits/stdc++.h>
using namespace std;
long long mod = 1e9 + 7;
vector<int> tree[50001];
int dp1[50001][501], dp2[50001][501];
long long ans = 0;
void dfs1(int source, int parent, int k) {
  dp1[source][0] = 1;
  for (auto e : tree[source]) {
    if (e != parent) dfs1(e, source, k);
  }
  for (int dist = 1; dist <= k; dist++) {
    dp1[source][dist] = 0;
    for (auto e : tree[source]) {
      if (e != parent) dp1[source][dist] += dp1[e][dist - 1];
    }
  }
}
void dfs2(int source, int parent, int k) {
  dp2[source][0] = dp1[source][0];
  for (int dist = 1; dist <= k; dist++) {
    dp2[source][dist] = dp1[source][dist];
    dp2[source][dist] += dp2[parent][dist - 1];
    if (dist > 1) dp2[source][dist] -= dp1[source][dist - 2];
  }
  for (auto e : tree[source]) {
    if (e != parent) dfs2(e, source, k);
  }
}
void solve() {
  int n, k;
  cin >> n >> k;
  int i1, i2;
  for (int i = 1; i < n; i++) {
    cin >> i1 >> i2;
    tree[i1].push_back(i2);
    tree[i2].push_back(i1);
  }
  dfs1(n, -1, k);
  for (int i = 0; i <= k; i++) dp2[n][i] = dp1[n][i];
  for (auto e : tree[n]) {
    dfs2(e, n, k);
  }
  for (int i = 1; i <= n; i++) {
    ans += dp2[i][k];
  }
  cout << ans / 2;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int _ = 1;
  ;
  while (_--) {
    solve();
  }
}

### 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;
long long mod = 1e9 + 7;
vector<int> tree[50001];
int dp1[50001][501], dp2[50001][501];
long long ans = 0;
void dfs1(int source, int parent, int k) {
  dp1[source][0] = 1;
  for (auto e : tree[source]) {
    if (e != parent) dfs1(e, source, k);
  }
  for (int dist = 1; dist <= k; dist++) {
    dp1[source][dist] = 0;
    for (auto e : tree[source]) {
      if (e != parent) dp1[source][dist] += dp1[e][dist - 1];
    }
  }
}
void dfs2(int source, int parent, int k) {
  dp2[source][0] = dp1[source][0];
  for (int dist = 1; dist <= k; dist++) {
    dp2[source][dist] = dp1[source][dist];
    dp2[source][dist] += dp2[parent][dist - 1];
    if (dist > 1) dp2[source][dist] -= dp1[source][dist - 2];
  }
  for (auto e : tree[source]) {
    if (e != parent) dfs2(e, source, k);
  }
}
void solve() {
  int n, k;
  cin >> n >> k;
  int i1, i2;
  for (int i = 1; i < n; i++) {
    cin >> i1 >> i2;
    tree[i1].push_back(i2);
    tree[i2].push_back(i1);
  }
  dfs1(n, -1, k);
  for (int i = 0; i <= k; i++) dp2[n][i] = dp1[n][i];
  for (auto e : tree[n]) {
    dfs2(e, n, k);
  }
  for (int i = 1; i <= n; i++) {
    ans += dp2[i][k];
  }
  cout << ans / 2;
}
int main() {
  ios::sync_with_stdio(0);
  cin.tie(0);
  int _ = 1;
  ;
  while (_--) {
    solve();
  }
}

```