#include <bits/stdc++.h>
using namespace std;
const int N = 50010, K = 510;
int cnt, head[N];
struct node {
  int v, nxt, w;
} e[N << 1];
void add(int u, int v) {
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  head[u] = cnt;
}
int n, k;
long long f[N][K], ans;
void DP(int u, int fa) {
  f[u][0] = 1;
  for (int i = head[u]; i; i = e[i].nxt) {
    int v = e[i].v;
    if (v == fa) continue;
    DP(v, u);
    for (int j = 1; j < k; j++) ans += f[u][j] * f[v][k - j - 1];
    for (int j = k; j >= 1; j--) f[u][j] += f[v][j - 1];
  }
  ans += f[u][k];
}
int main() {
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    add(u, v);
    add(v, u);
  }
  DP(1, 0);
  cout << ans;
  return 0;
}

### 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;
const int N = 50010, K = 510;
int cnt, head[N];
struct node {
  int v, nxt, w;
} e[N << 1];
void add(int u, int v) {
  e[++cnt].nxt = head[u];
  e[cnt].v = v;
  head[u] = cnt;
}
int n, k;
long long f[N][K], ans;
void DP(int u, int fa) {
  f[u][0] = 1;
  for (int i = head[u]; i; i = e[i].nxt) {
    int v = e[i].v;
    if (v == fa) continue;
    DP(v, u);
    for (int j = 1; j < k; j++) ans += f[u][j] * f[v][k - j - 1];
    for (int j = k; j >= 1; j--) f[u][j] += f[v][j - 1];
  }
  ans += f[u][k];
}
int main() {
  cin >> n >> k;
  for (int i = 1; i < n; i++) {
    int u, v;
    cin >> u >> v;
    add(u, v);
    add(v, u);
  }
  DP(1, 0);
  cout << ans;
  return 0;
}

```