For some array c, let's denote a greedy subsequence as a sequence of indices p_1, p_2, ..., p_l such that 1 ≤ p_1 < p_2 < ... < p_l ≤ |c|, and for each i ∈ [1, l - 1], p_{i + 1} is the minimum number such that p_{i + 1} > p_i and c[p_{i + 1}] > c[p_i].

You are given an array a_1, a_2, ..., a_n. For each its subsegment of length k, calculate the length of its longest greedy subsequence.

Input

The first line contains two integers n and k (1 ≤ k ≤ n ≤ 10^6) — the length of array a and the length of subsegments.

The second line contains n integers a_1, a_2, ..., a_n (1 ≤ a_i ≤ n) — array a.

Output

Print n - k + 1 integers — the maximum lengths of greedy subsequences of each subsegment having length k. The first number should correspond to subsegment a[1..k], the second — to subsegment a[2..k + 1], and so on.

Examples

Input


6 4
1 5 2 5 3 6


Output


2 2 3 


Input


7 6
4 5 2 5 3 6 6


Output


3 3 

Note

In the first example: 

  * [1, 5, 2, 5] — the longest greedy subsequences are 1, 2 ([c_1, c_2] = [1, 5]) or 3, 4 ([c_3, c_4] = [2, 5]). 
  * [5, 2, 5, 3] — the sequence is 2, 3 ([c_2, c_3] = [2, 5]). 
  * [2, 5, 3, 6] — the sequence is 1, 2, 4 ([c_1, c_2, c_4] = [2, 5, 6]). 



In the second example: 

  * [4, 5, 2, 5, 3, 6] — the longest greedy subsequences are 1, 2, 6 ([c_1, c_2, c_6] = [4, 5, 6]) or 3, 4, 6 ([c_3, c_4, c_6] = [2, 5, 6]). 
  * [5, 2, 5, 3, 6, 6] — the subsequence is 2, 3, 5 ([c_2, c_3, c_5] = [2, 5, 6]). 
#include <bits/stdc++.h>
using namespace std;
using ll = long long int;
template <typename T>
ostream &operator+(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out << x << " ";
  }
  out << "\n";
  return out;
}
template <typename T>
ostream &operator*(ostream &out, const vector<T> &vec) {
  for (const auto &x : vec) {
    out + x;
  }
  return out;
}
template <typename T>
istream &operator>>(istream &in, vector<T> &vec) {
  for (auto &x : vec) {
    in >> x;
  }
  return in;
}
struct Tree {
  int n;
  vector<vector<int>> adj;
  Tree(int n) : n(n) { adj.resize(n); }
  void addedge(int u, int v) {
    adj[u].push_back(v);
    adj[v].push_back(u);
  }
};
struct EulerTour : Tree {
 private:
  int t;
  void dfs(int u, int p) {
    tin[u] = t++;
    eulertour.push_back(u);
    for (const auto &v : adj[u]) {
      if (v != p) dfs(v, u);
    }
    tout[u] = t++;
    eulertour.push_back(u);
  }

 public:
  vector<int> tin, tout, eulertour;
  void ComputeEulerTour(int root = 0) {
    t = 0;
    tin.resize(n), tout.resize(n), eulertour.reserve(n << 1);
    dfs(root, root);
  }
  bool isanc(int u, int v) { return tin[u] <= tin[v] && tout[u] >= tout[v]; }
  EulerTour(int n) : Tree(n) {}
};
template <typename T, typename U>
struct lazy_segment_tree {
  int n;
  int H;
  T base;
  vector<T> segtree;
  vector<U> lazytree;
  vector<bool> isempty;
  function<T(const T &, const T &)> join;
  function<T(int, const U &, const T &)> assign;
  function<U(const U &, const U &)> lazyassign;
  lazy_segment_tree(vector<T> &seq, function<T(const T &, const T &)> join,
                    function<T(int, const U &, const T &)> assign,
                    function<U(const U &, const U &)> lazyassign, T base)
      : join(join), assign(assign), lazyassign(lazyassign), base(base) {
    n = seq.size();
    H = 32 - __builtin_clz(n);
    segtree.resize(2 * n);
    lazytree.resize(n);
    isempty.resize(n, 1);
    for (int i = 0; i < n; i++) {
      segtree[n + i] = seq[i];
    }
    for (int i = n - 1; i >= 1; i--) {
      segtree[i] = join(segtree[(i << 1)], segtree[(i << 1) | 1]);
    }
  }
  lazy_segment_tree(int n, function<T(const T &, const T &)> join,
                    function<T(int, const U &, const T &)> assign,
                    function<U(const U &, const U &)> lazyassign, T base)
      : join(join), assign(assign), lazyassign(lazyassign), base(base), n(n) {
    H = 32 - __builtin_clz(n);
    segtree.resize(2 * n);
    lazytree.resize(n);
    isempty.resize(n, 1);
  }
  void calc(int pos, int h) {
    segtree[pos] = join(segtree[(pos << 1)], segtree[(pos << 1) | 1]);
    if (!isempty[pos]) {
      segtree[pos] = assign(h, lazytree[pos], segtree[pos]);
    }
  }
  void apply(int pos, U value, int h) {
    segtree[pos] = assign(h, value, segtree[pos]);
    if (pos < n) {
      if (!isempty[pos]) {
        lazytree[pos] = lazyassign(value, lazytree[pos]);
      } else {
        lazytree[pos] = value;
      }
      isempty[pos] = 0;
    }
  }
  void updatenode(int pos) {
    int h = 0;
    pos += n;
    while (pos > 1) {
      h++;
      pos >>= 1;
      calc(pos, h);
    }
  }
  void push(int pos) {
    int h = H;
    for (pos += n; h; --h) {
      int x = (pos >> h);
      if (!isempty[x]) {
        apply((x << 1), lazytree[x], h - 1);
        apply((x << 1) | 1, lazytree[x], h - 1);
        isempty[x] = 1;
      }
    }
  }
  void updaterange(int l, int r, U value) {
    push(l);
    push(r);
    int k = 0;
    int l0 = l, r0 = r;
    for (l += n, r += n + 1; l < r; l >>= 1, r >>= 1, k++) {
      if (l & 1) {
        apply(l++, value, k);
      }
      if (r & 1) {
        apply(--r, value, k);
      }
    }
    updatenode(l0);
    updatenode(r0);
  }
  T query(int l, int r) {
    push(l);
    push(r);
    T ansl = base;
    T ansr = base;
    for (l += n, r += n + 1; l < r; l >>= 1, r >>= 1) {
      if (l & 1) {
        ansl = join(ansl, segtree[l++]);
      }
      if (r & 1) {
        ansr = join(segtree[--r], ansr);
      }
    }
    return join(ansl, ansr);
  }
};
const int INF = 1e9;
void solve() {
  int n, k;
  cin >> n >> k;
  vector<int> seq(n);
  cin >> seq;
  EulerTour tree(n + 1);
  stack<int> values;
  for (int i = n - 1; i >= 0; --i) {
    while (!values.empty() && seq[values.top()] <= seq[i]) {
      values.pop();
    }
    if (values.empty()) {
      tree.addedge(i, n);
    } else {
      tree.addedge(i, values.top());
    }
    values.push(i);
  }
  tree.ComputeEulerTour(n);
  lazy_segment_tree<ll, ll> segtree(
      2 * n + 2, [&](ll x, ll y) { return max(x, y); },
      [&](int h, ll l, ll x) { return l + x; },
      [&](ll x, ll y) { return x + y; }, -INF);
  for (int i = 0; i < k; i++) {
    segtree.updaterange(tree.tin[i], tree.tout[i], 1);
  }
  cout << segtree.query(0, 2 * n + 1) << " ";
  for (int i = k; i < n; i++) {
    segtree.updaterange(tree.tin[i - k], tree.tout[i - k], -INF);
    segtree.updaterange(tree.tin[i], tree.tout[i], 1);
    cout << segtree.query(0, 2 * n + 1) << " ";
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  solve();
}
