#include <bits/stdc++.h>
struct {
  int to, next;
} edge[100100];
int head[50100];
long long dps[50100][550];
int cnt, k;
long long ans;
void add(int a, int b) {
  edge[cnt].to = b;
  edge[cnt].next = head[a];
  head[a] = cnt++;
  edge[cnt].to = a;
  edge[cnt].next = head[b];
  head[b] = cnt++;
}
void dp(int u, int p) {
  int i, j;
  dps[u][0] = 1;
  for (i = head[u]; i; i = edge[i].next) {
    int v = edge[i].to;
    if (v == p) continue;
    dp(v, u);
    for (j = 0; j < k; j++) ans += dps[u][j] * dps[v][k - j - 1];
    for (j = 1; j <= k; j++) dps[u][j] += dps[v][j - 1];
  }
}
int main() {
  int i, j, n, a, b;
  scanf("%d %d", &n, &k);
  cnt = 1;
  for (i = 1; i < n; i++) {
    scanf("%d %d", &a, &b);
    add(a, b);
  }
  dp(1, 0);
  printf("%I64d\n", ans);
}

### Prompt

Generate 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>
struct {
  int to, next;
} edge[100100];
int head[50100];
long long dps[50100][550];
int cnt, k;
long long ans;
void add(int a, int b) {
  edge[cnt].to = b;
  edge[cnt].next = head[a];
  head[a] = cnt++;
  edge[cnt].to = a;
  edge[cnt].next = head[b];
  head[b] = cnt++;
}
void dp(int u, int p) {
  int i, j;
  dps[u][0] = 1;
  for (i = head[u]; i; i = edge[i].next) {
    int v = edge[i].to;
    if (v == p) continue;
    dp(v, u);
    for (j = 0; j < k; j++) ans += dps[u][j] * dps[v][k - j - 1];
    for (j = 1; j <= k; j++) dps[u][j] += dps[v][j - 1];
  }
}
int main() {
  int i, j, n, a, b;
  scanf("%d %d", &n, &k);
  cnt = 1;
  for (i = 1; i < n; i++) {
    scanf("%d %d", &a, &b);
    add(a, b);
  }
  dp(1, 0);
  printf("%I64d\n", ans);
}

```