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;
const int N = int(1e6 + 10);
int a[N];
set<pair<int, int> > mst;
int in[N], out[N];
int n, k;
int T = 1;
vector<int> adj[N];
void dfs(int u) {
  in[u] = T;
  for (int v : adj[u]) {
    T++;
    dfs(v);
  }
  out[u] = T;
}
int segtree[N << 3];
int lazzy[N << 3];
void push(int node) {
  segtree[node] += lazzy[node];
  int lf = node << 1;
  int rg = lf + 1;
  lazzy[lf] += lazzy[node];
  lazzy[rg] += lazzy[node];
  lazzy[node] = 0;
}
void update(int node, int i, int j, int l, int r, int val) {
  if (lazzy[node]) {
    push(node);
  }
  if (i > r || j < l) {
    return;
  }
  if (l <= i && j <= r) {
    lazzy[node] += val;
    push(node);
  } else {
    int mid = (i + j) >> 1;
    int lf = node << 1;
    int rg = lf + 1;
    update(lf, i, mid, l, r, val);
    update(rg, mid + 1, j, l, r, val);
    segtree[node] = max(segtree[lf], segtree[rg]);
  }
}
int main() {
  ios::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
    while (mst.size() && (*mst.begin()).first < a[i]) {
      adj[i].push_back((*mst.begin()).second);
      mst.erase(mst.begin());
    }
    mst.insert({a[i], i});
  }
  while (mst.size()) {
    adj[n + 1].push_back((*mst.begin()).second);
    mst.erase(mst.begin());
  }
  dfs(n + 1);
  for (int i = 1; i <= k - 1; i++) {
    update(1, 1, n + 1, in[i], out[i], 1);
  }
  for (int i = k; i <= n; i++) {
    update(1, 1, n + 1, in[i], out[i], 1);
    cout << segtree[1] << " ";
    update(1, 1, n + 1, in[i - k + 1], out[i - k + 1], -1);
  }
  cout << endl;
  return 0;
}
