#include <bits/stdc++.h>
using namespace std;
int read() {
  int f = 1, x = 0;
  char c = getchar();
  while (c < '0' || '9' < c) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while ('0' <= c && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return f * x;
}
struct Edge {
  int v, nxt;
} edge[2 * 100000 + 5];
int ecnt, head[100000 + 5];
void Addedge(int u, int v) {
  edge[++ecnt] = (Edge){v, head[u]}, head[u] = ecnt;
  edge[++ecnt] = (Edge){u, head[v]}, head[v] = ecnt;
  return;
}
int n, k;
bool vis[100000 + 5];
int sum, mx, root, siz[100000 + 5];
void GetRoot(int u, int fa) {
  siz[u] = 1;
  int Maxson = 0;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (v == fa || vis[v]) continue;
    GetRoot(v, u), siz[u] += siz[v];
    Maxson = max(Maxson, siz[v]);
  }
  Maxson = max(Maxson, sum - siz[u]);
  if (Maxson < mx) mx = Maxson, root = u;
  return;
}
long long ans;
int cnt[100000 + 5];
void Addson(int u, int fa, int type, int d) {
  if (type == 0) {
    if (k >= d) ans += cnt[k - d];
  } else
    cnt[d] += type;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (v == fa || vis[v]) continue;
    Addson(v, u, type, d + 1);
  }
  return;
}
void Cal(int u) {
  cnt[0]++;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    Addson(v, 0, 0, 1), Addson(v, 0, 1, 1);
  }
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    Addson(v, 0, -1, 1);
  }
  cnt[0]--;
  return;
}
void DFS(int u) {
  vis[u] = 1, Cal(u);
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    sum = siz[v], mx = 0x3f3f3f3f, GetRoot(v, 0);
    DFS(root);
  }
  return;
}
int main() {
  n = read(), k = read();
  for (int i = 1; i < n; i++) {
    int u = read(), v = read();
    Addedge(u, v);
  }
  sum = n, mx = 0x3f3f3f3f, GetRoot(1, 0);
  DFS(root);
  printf("%lld\n", ans);
  return 0;
}

### Prompt

Please create a solution in Cpp 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;
int read() {
  int f = 1, x = 0;
  char c = getchar();
  while (c < '0' || '9' < c) {
    if (c == '-') f = -1;
    c = getchar();
  }
  while ('0' <= c && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return f * x;
}
struct Edge {
  int v, nxt;
} edge[2 * 100000 + 5];
int ecnt, head[100000 + 5];
void Addedge(int u, int v) {
  edge[++ecnt] = (Edge){v, head[u]}, head[u] = ecnt;
  edge[++ecnt] = (Edge){u, head[v]}, head[v] = ecnt;
  return;
}
int n, k;
bool vis[100000 + 5];
int sum, mx, root, siz[100000 + 5];
void GetRoot(int u, int fa) {
  siz[u] = 1;
  int Maxson = 0;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (v == fa || vis[v]) continue;
    GetRoot(v, u), siz[u] += siz[v];
    Maxson = max(Maxson, siz[v]);
  }
  Maxson = max(Maxson, sum - siz[u]);
  if (Maxson < mx) mx = Maxson, root = u;
  return;
}
long long ans;
int cnt[100000 + 5];
void Addson(int u, int fa, int type, int d) {
  if (type == 0) {
    if (k >= d) ans += cnt[k - d];
  } else
    cnt[d] += type;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (v == fa || vis[v]) continue;
    Addson(v, u, type, d + 1);
  }
  return;
}
void Cal(int u) {
  cnt[0]++;
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    Addson(v, 0, 0, 1), Addson(v, 0, 1, 1);
  }
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    Addson(v, 0, -1, 1);
  }
  cnt[0]--;
  return;
}
void DFS(int u) {
  vis[u] = 1, Cal(u);
  for (int i = head[u]; i; i = edge[i].nxt) {
    int v = edge[i].v;
    if (vis[v]) continue;
    sum = siz[v], mx = 0x3f3f3f3f, GetRoot(v, 0);
    DFS(root);
  }
  return;
}
int main() {
  n = read(), k = read();
  for (int i = 1; i < n; i++) {
    int u = read(), v = read();
    Addedge(u, v);
  }
  sum = n, mx = 0x3f3f3f3f, GetRoot(1, 0);
  DFS(root);
  printf("%lld\n", ans);
  return 0;
}

```