#include <bits/stdc++.h>
using namespace std;
struct edge {
  int link, next;
} e[100010];
int n, k, f[50010][510], h[100010], jud[50010], tt = 0;
long long ans[50010], tot;
void addEdge(int x, int y) {
  tt++;
  e[tt].link = y;
  e[tt].next = h[x];
  h[x] = tt;
}
void dfs(int x) {
  jud[x] = 1;
  f[x][0] = 1;
  for (int i = h[x]; i != 0; i = e[i].next)
    if (jud[e[i].link] == 0) {
      int y = e[i].link;
      dfs(y);
      for (int j = 0; j < k; j++)
        ans[x] = ans[x] + 1LL * f[x][j] * f[y][k - j - 1];
      for (int j = 0; j < k; j++) f[x][j + 1] += f[y][j];
    }
  tot += ans[x];
  return;
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i < n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    addEdge(a, b);
    addEdge(b, a);
  }
  memset(jud, 0, sizeof(jud));
  dfs(1);
  cout << tot << endl;
  return 0;
}

### Prompt

Develop a solution in cpp to the problem described below:

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;
struct edge {
  int link, next;
} e[100010];
int n, k, f[50010][510], h[100010], jud[50010], tt = 0;
long long ans[50010], tot;
void addEdge(int x, int y) {
  tt++;
  e[tt].link = y;
  e[tt].next = h[x];
  h[x] = tt;
}
void dfs(int x) {
  jud[x] = 1;
  f[x][0] = 1;
  for (int i = h[x]; i != 0; i = e[i].next)
    if (jud[e[i].link] == 0) {
      int y = e[i].link;
      dfs(y);
      for (int j = 0; j < k; j++)
        ans[x] = ans[x] + 1LL * f[x][j] * f[y][k - j - 1];
      for (int j = 0; j < k; j++) f[x][j + 1] += f[y][j];
    }
  tot += ans[x];
  return;
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i < n; i++) {
    int a, b;
    scanf("%d%d", &a, &b);
    addEdge(a, b);
    addEdge(b, a);
  }
  memset(jud, 0, sizeof(jud));
  dfs(1);
  cout << tot << endl;
  return 0;
}

```