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;
int better(int a, int b, const vector<int>& depth,
           const vector<vector<int>>& par) {
  if (depth[a] >= depth[b]) return 2 * depth.size();
  int sb = b;
  for (int i = 19; i >= 0; --i)
    if (par[b][i] != -1 && depth[par[b][i]] >= depth[a]) b = par[b][i];
  for (int i = 19; i >= 0; --i)
    if (par[a][i] != -1 && par[b][i] != -1 && par[a][i] != par[b][i]) {
      a = par[a][i];
      b = par[b][i];
      sb = par[sb][i];
    }
  return par[sb][0];
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  int n, k;
  cin >> n >> k;
  vector<int> a(n);
  for (auto& x : a) cin >> x;
  vector<int> f(n, -1);
  vector<int> depth(n, 0);
  vector<int> stk;
  for (int i = n - 1; i >= 0; --i) {
    while (stk.size() > 0 && a[stk.back()] <= a[i]) stk.pop_back();
    if (stk.size() > 0) {
      f[i] = stk.back();
      depth[i] = depth[f[i]] + 1;
    }
    stk.push_back(i);
  }
  vector<vector<int>> par(n, vector<int>(20, -1));
  for (int i = 0; i < n; ++i) par[i][0] = f[i];
  for (int s = 1; s < 20; ++s)
    for (int i = 0; i < n; ++i)
      if (par[i][s - 1] != -1) {
        par[i][s] = par[par[i][s - 1]][s - 1];
      }
  deque<int> q;
  vector<int> res;
  for (int i = n - 1; i >= 0; --i) {
    while (q.size() > 1 && better(q[1], q[0], depth, par) >= i + k) {
      q.pop_front();
    }
    while (q.size() > 0) {
      int x = better(i, q.back(), depth, par);
      if (x >= i + k) {
        q.pop_back();
        continue;
      }
      if (q.size() == 1) break;
      int y = better(q.back(), q[q.size() - 2], depth, par);
      if (x >= y) {
        q.pop_back();
        continue;
      }
      break;
    }
    q.push_back(i);
    if (i + k <= n) {
      int x = q.front();
      int cnt = 0;
      for (int j = 19; j >= 0; --j) {
        if (par[x][j] != -1 && par[x][j] < i + k) {
          cnt += 1 << j;
          x = par[x][j];
        }
      }
      res.push_back(cnt);
    }
  }
  for (int i = res.size() - 1; i >= 0; --i) cout << res[i] + 1 << " ";
  cout << endl;
  return 0;
}
