#include <bits/stdc++.h>
using namespace std;
vector<int> rel[50005];
queue<int> topo;
int nodes, dist, n1, n2, node, totes, rtotes;
int dp[50005][505], vis[50005], parent[50005], nsort[50005];
bool hp(int i, int j) { return vis[i] > vis[j]; }
int main() {
  scanf("%d%d", &nodes, &dist);
  for (int i = 1; i < nodes; i++) {
    scanf("%d%d", &n1, &n2);
    dp[i][0] = 1;
    nsort[i] = i;
    rel[n1].push_back(n2);
    rel[n2].push_back(n1);
  }
  dp[nodes][0] = 1;
  nsort[nodes] = nodes;
  topo.push(1);
  vis[1] = 1;
  while (!topo.empty()) {
    node = topo.front();
    topo.pop();
    for (int i = 0; i < rel[node].size(); i++) {
      if (!vis[rel[node][i]]) {
        parent[rel[node][i]] = node;
        vis[rel[node][i]] = vis[node] + 1;
        topo.push(rel[node][i]);
      }
    }
  }
  sort(nsort + 1, nsort + 1 + nodes, hp);
  for (int i = 1; i <= nodes; i++) {
    node = nsort[i];
    for (int j = 0; j < dist; j++) {
      rtotes += dp[node][j] * dp[parent[node]][dist - j - 1];
    }
    dp[parent[node]][0] = 1;
    for (int j = 0; j <= dist; j++) {
      dp[parent[node]][j + 1] += dp[node][j];
    }
    if (parent[node]) {
      topo.push(parent[node]);
    }
  }
  printf("%d\n", rtotes);
  return 0;
}

### Prompt

Please provide a cpp coded solution 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;
vector<int> rel[50005];
queue<int> topo;
int nodes, dist, n1, n2, node, totes, rtotes;
int dp[50005][505], vis[50005], parent[50005], nsort[50005];
bool hp(int i, int j) { return vis[i] > vis[j]; }
int main() {
  scanf("%d%d", &nodes, &dist);
  for (int i = 1; i < nodes; i++) {
    scanf("%d%d", &n1, &n2);
    dp[i][0] = 1;
    nsort[i] = i;
    rel[n1].push_back(n2);
    rel[n2].push_back(n1);
  }
  dp[nodes][0] = 1;
  nsort[nodes] = nodes;
  topo.push(1);
  vis[1] = 1;
  while (!topo.empty()) {
    node = topo.front();
    topo.pop();
    for (int i = 0; i < rel[node].size(); i++) {
      if (!vis[rel[node][i]]) {
        parent[rel[node][i]] = node;
        vis[rel[node][i]] = vis[node] + 1;
        topo.push(rel[node][i]);
      }
    }
  }
  sort(nsort + 1, nsort + 1 + nodes, hp);
  for (int i = 1; i <= nodes; i++) {
    node = nsort[i];
    for (int j = 0; j < dist; j++) {
      rtotes += dp[node][j] * dp[parent[node]][dist - j - 1];
    }
    dp[parent[node]][0] = 1;
    for (int j = 0; j <= dist; j++) {
      dp[parent[node]][j + 1] += dp[node][j];
    }
    if (parent[node]) {
      topo.push(parent[node]);
    }
  }
  printf("%d\n", rtotes);
  return 0;
}

```