Problem: You are given an undirected tree, consisting of n vertices.

The vertex is called a leaf if it has exactly one vertex adjacent to it.

The distance between some pair of vertices is the number of edges in the shortest path between them.

Let's call some set of leaves beautiful if the maximum distance between any pair of leaves in it is less or equal to k.

You want to split all leaves into non-intersecting beautiful sets. What is the minimal number of sets in such a split?

Input

The first line contains two integers n and k (3 ≤ n ≤ 10^6, 1 ≤ k ≤ 10^6) — the number of vertices in the tree and the maximum distance between any pair of leaves in each beautiful set.

Each of the next n - 1 lines contains two integers v_i and u_i (1 ≤ v_i, u_i ≤ n) — the description of the i-th edge. 

It is guaranteed that the given edges form a tree.

Output

Print a single integer — the minimal number of beautiful sets the split can have. 

Examples

Input

9 3
1 2
1 3
2 4
2 5
3 6
6 7
6 8
3 9


Output

2


Input

5 3
1 2
2 3
3 4
4 5


Output

2


Input

6 1
1 2
1 3
1 4
1 5
1 6


Output

5

Note

Here is the graph for the first example:

<image>

Solution (in CPP):

Solution:
#include <bits/stdc++.h>
using namespace std;
template <typename T, typename U>
inline void smin(T &a, const U &b) {
  if (a > b) a = b;
}
template <typename T, typename U>
inline void smax(T &a, const U &b) {
  if (a < b) a = b;
}
template <class T>
inline void gn(T &first) {
  char c, sg = 0;
  while (c = getchar(), (c > '9' || c < '0') && c != '-')
    ;
  for ((c == '-' ? sg = 1, c = getchar() : 0), first = 0; c >= '0' && c <= '9';
       c = getchar())
    first = (first << 1) + (first << 3) + c - '0';
  if (sg) first = -first;
}
template <class T1, class T2>
inline void gn(T1 &x1, T2 &x2) {
  gn(x1), gn(x2);
}
template <class T1, class T2, class T3>
inline void gn(T1 &x1, T2 &x2, T3 &x3) {
  gn(x1, x2), gn(x3);
}
template <class T1, class T2, class T3, class T4>
inline void gn(T1 &x1, T2 &x2, T3 &x3, T4 &x4) {
  gn(x1, x2), gn(x3, x4);
}
template <class T>
inline void print(T first) {
  if (first < 0) {
    putchar('-');
    return print(-first);
  }
  if (first < 10) {
    putchar('0' + first);
    return;
  }
  print(first / 10);
  putchar(first % 10 + '0');
}
template <class T>
inline void println(T first) {
  print(first);
  putchar('\n');
}
template <class T>
inline void printsp(T first) {
  print(first);
  putchar(' ');
}
template <class T1, class T2>
inline void print(T1 x1, T2 x2) {
  printsp(x1), println(x2);
}
template <class T1, class T2, class T3>
inline void print(T1 x1, T2 x2, T3 x3) {
  printsp(x1), printsp(x2), println(x3);
}
template <class T1, class T2, class T3, class T4>
inline void print(T1 x1, T2 x2, T3 x3, T4 x4) {
  printsp(x1), printsp(x2), printsp(x3), println(x4);
}
int power(int a, int b, int m, int ans = 1) {
  for (; b; b >>= 1, a = (long long)a * a % m)
    if (b & 1) ans = (long long)ans * a % m;
  return ans;
}
vector<int> adj[1001000], a[1001000];
int pa[1001000], dp[1001000], mx;
void dfs(int u) {
  smax(mx, dp[u]);
  if (adj[u].size() == 1) a[dp[u]].push_back(u);
  for (int i = adj[u].size(); i--;) {
    int v = adj[u][i];
    if (v != pa[u]) {
      pa[v] = u;
      dp[v] = dp[u] + 1;
      dfs(v);
    }
  }
}
int root[1001000], len[1001000];
int find_root(int u) {
  if (u == root[u]) return u;
  return root[u] = find_root(root[u]);
}
bool cmp(int u, int v) { return len[u] > len[v]; }
int main() {
  int n, k;
  gn(n, k);
  for (int i = 1, u, v; i < n; i++) {
    gn(u, v);
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
  for (int i = 1; i <= n; i++)
    if (adj[i].size() > 1) {
      dp[i] = 1;
      dfs(i);
      break;
    }
  for (int i = 1; i <= n; i++) root[i] = i;
  for (int i = mx; i >= 1; i--) {
    sort(a[i].begin(), a[i].end(), cmp);
    a[i].resize(unique(a[i].begin(), a[i].end()) - a[i].begin());
    for (int j = a[i].size(); j--;) {
      int u = a[i][j], fa = pa[u];
      if (len[fa] + len[u] + 1 <= k) {
        root[u] = fa;
        smax(len[fa], len[u] + 1);
        a[dp[fa]].push_back(fa);
      }
    }
  }
  set<int> s;
  for (int i = 1; i <= n; i++)
    if (adj[i].size() == 1) {
      s.insert(find_root(i));
    }
  println(s.size());
}