#include <bits/stdc++.h>
using namespace std;
const long long MOD = 1e9 + 7;
const long double PI = 3.141592653589793238462643383279502884197;
priority_queue<int, vector<int>, greater<int> > pq;
vector<int> v[50000];
int tree[50000][501];
int pp[50000];
int k;
void gogo(int o, int p) {
  pp[o] = p;
  for (int i = 0; i < (int)(v[o]).size(); i++) {
    if (p == v[o][i]) continue;
    gogo(v[o][i], o);
  }
}
long long go(int o, int p) {
  int vec[501] = {0};
  int x = o;
  for (int i = 0; i <= k; i++) {
    tree[x][i]++;
    x = pp[x];
    if (x == -1) break;
  }
  vec[0]++;
  long long sum = 0;
  for (int i = 0; i < (int)(v[o]).size(); i++) {
    if (v[o][i] == p) continue;
    sum += go(v[o][i], o);
    for (int j = 0; j <= k; j++) {
      sum += ((long long)tree[o][j] - vec[j]) * vec[k - j];
    }
    for (int j = 0; j <= k; j++) vec[j] = tree[o][j];
  }
  return sum;
}
int main() {
  int n;
  scanf("%d %d", &n, &k);
  int a, b;
  for (int i = 0; i < n - 1; i++) {
    scanf("%d %d", &a, &b);
    a--;
    b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  gogo(0, -1);
  printf("%lld", go(0, 0));
}

### Prompt

Your challenge is to write 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;
const long long MOD = 1e9 + 7;
const long double PI = 3.141592653589793238462643383279502884197;
priority_queue<int, vector<int>, greater<int> > pq;
vector<int> v[50000];
int tree[50000][501];
int pp[50000];
int k;
void gogo(int o, int p) {
  pp[o] = p;
  for (int i = 0; i < (int)(v[o]).size(); i++) {
    if (p == v[o][i]) continue;
    gogo(v[o][i], o);
  }
}
long long go(int o, int p) {
  int vec[501] = {0};
  int x = o;
  for (int i = 0; i <= k; i++) {
    tree[x][i]++;
    x = pp[x];
    if (x == -1) break;
  }
  vec[0]++;
  long long sum = 0;
  for (int i = 0; i < (int)(v[o]).size(); i++) {
    if (v[o][i] == p) continue;
    sum += go(v[o][i], o);
    for (int j = 0; j <= k; j++) {
      sum += ((long long)tree[o][j] - vec[j]) * vec[k - j];
    }
    for (int j = 0; j <= k; j++) vec[j] = tree[o][j];
  }
  return sum;
}
int main() {
  int n;
  scanf("%d %d", &n, &k);
  int a, b;
  for (int i = 0; i < n - 1; i++) {
    scanf("%d %d", &a, &b);
    a--;
    b--;
    v[a].push_back(b);
    v[b].push_back(a);
  }
  gogo(0, -1);
  printf("%lld", go(0, 0));
}

```