#include <bits/stdc++.h>
using namespace std;
class edges {
 public:
  int v, next;
} edge[50050 << 1];
long long f[50050][505];
int n, lnk[50050], vst[50050];
int N, K;
long long ans = 0;
void add(int u, int v) {
  edge[n].v = v;
  edge[n].next = lnk[u];
  lnk[u] = n++;
}
void dfs(int rt) {
  vst[rt] = 1;
  f[rt][0] = 1;
  for (int i = lnk[rt]; ~i; i = edge[i].next) {
    int j = edge[i].v;
    if (vst[j]) continue;
    dfs(j);
    for (int i = 1; i < K; i++) {
      ans += f[rt][i] * f[j][K - i - 1];
    }
    f[rt][1]++;
    for (int i = 2; i <= K; i++) {
      f[rt][i] += f[j][i - 1];
    }
  }
  ans += f[rt][K];
}
int main() {
  cin >> N >> K;
  memset(lnk, -1, sizeof(lnk));
  for (int i = 1; i < N; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    add(a, b);
    add(b, a);
  }
  dfs(1);
  cout << ans << endl;
  return 0;
}

### 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;
class edges {
 public:
  int v, next;
} edge[50050 << 1];
long long f[50050][505];
int n, lnk[50050], vst[50050];
int N, K;
long long ans = 0;
void add(int u, int v) {
  edge[n].v = v;
  edge[n].next = lnk[u];
  lnk[u] = n++;
}
void dfs(int rt) {
  vst[rt] = 1;
  f[rt][0] = 1;
  for (int i = lnk[rt]; ~i; i = edge[i].next) {
    int j = edge[i].v;
    if (vst[j]) continue;
    dfs(j);
    for (int i = 1; i < K; i++) {
      ans += f[rt][i] * f[j][K - i - 1];
    }
    f[rt][1]++;
    for (int i = 2; i <= K; i++) {
      f[rt][i] += f[j][i - 1];
    }
  }
  ans += f[rt][K];
}
int main() {
  cin >> N >> K;
  memset(lnk, -1, sizeof(lnk));
  for (int i = 1; i < N; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    add(a, b);
    add(b, a);
  }
  dfs(1);
  cout << ans << endl;
  return 0;
}

```