#include <bits/stdc++.h>
struct Nodo {
  int a;
  int sgte;
} Nodo[100100];
long long aux[50010][510];
long long int cont;
int dir[50001];
int n, k;
void agregar(int x, int y, int c);
void busqueda(int fa, int u);
int main() {
  int x, y, i, t, cargado = 0;
  scanf("%d %d", &n, &k);
  for (t = 0; t < 50010; t++) {
    dir[t] = -1;
  }
  for (i = 0; i < (n - 1); i++) {
    scanf("%d %d", &x, &y);
    agregar(x, y, cargado);
    cargado++;
    agregar(y, x, cargado);
    cargado++;
  }
  busqueda(0, 1);
  printf("%I64d", cont);
  return 0;
}
void busqueda(int ant, int act) {
  int i = 0, v, j;
  aux[act][0] = 1;
  for (i = dir[act]; i != -1; i = Nodo[i].sgte) {
    v = Nodo[i].a;
    if (ant != v) {
      busqueda(act, v);
      for (j = 0; j < k; j++) {
        cont += aux[act][j] * aux[v][k - j - 1];
      }
      for (j = 1; j <= k; j++) {
        aux[act][j] += aux[v][j - 1];
      }
    }
  }
}
void agregar(int x, int y, int c) {
  Nodo[c].a = y;
  Nodo[c].sgte = dir[x];
  dir[x] = c;
}

### Prompt

Develop a solution in CPP 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>
struct Nodo {
  int a;
  int sgte;
} Nodo[100100];
long long aux[50010][510];
long long int cont;
int dir[50001];
int n, k;
void agregar(int x, int y, int c);
void busqueda(int fa, int u);
int main() {
  int x, y, i, t, cargado = 0;
  scanf("%d %d", &n, &k);
  for (t = 0; t < 50010; t++) {
    dir[t] = -1;
  }
  for (i = 0; i < (n - 1); i++) {
    scanf("%d %d", &x, &y);
    agregar(x, y, cargado);
    cargado++;
    agregar(y, x, cargado);
    cargado++;
  }
  busqueda(0, 1);
  printf("%I64d", cont);
  return 0;
}
void busqueda(int ant, int act) {
  int i = 0, v, j;
  aux[act][0] = 1;
  for (i = dir[act]; i != -1; i = Nodo[i].sgte) {
    v = Nodo[i].a;
    if (ant != v) {
      busqueda(act, v);
      for (j = 0; j < k; j++) {
        cont += aux[act][j] * aux[v][k - j - 1];
      }
      for (j = 1; j <= k; j++) {
        aux[act][j] += aux[v][j - 1];
      }
    }
  }
}
void agregar(int x, int y, int c) {
  Nodo[c].a = y;
  Nodo[c].sgte = dir[x];
  dir[x] = c;
}

```