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 n, k;
vector<int> a;
int T = 0;
vector<vector<int> > g;
vector<int> tin, tout;
void dfs(int v) {
  tin[v] = T++;
  for (int i = 0; i < g[v].size(); i++) {
    dfs(g[v][i]);
  }
  tout[v] = T;
}
vector<int> tmax, tadd;
void push(int v) {
  tadd[2 * v + 1] += tadd[v];
  tadd[2 * v + 2] += tadd[v];
  tadd[v] = 0;
}
int getmax(int v) { return tmax[v] + tadd[v]; }
void add(int v, int l, int r, int lf, int rg, int val) {
  if (l == lf && r == rg) {
    tadd[v] += val;
    return;
  }
  int m = (l + r) / 2;
  push(v);
  if (lf < m) add(2 * v + 1, l, m, lf, min(m, rg), val);
  if (rg > m) add(2 * v + 2, m, r, max(lf, m), rg, val);
  tmax[v] = max(getmax(2 * v + 1), getmax(2 * v + 2));
}
int main() {
  cin.tie(NULL);
  cout.tie(NULL);
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  a.assign(n, 0);
  for (int i = 0; i < n; i++) {
    cin >> a[i];
  }
  g.resize(n + 1);
  tin.resize(n + 1, 0);
  tout.resize(n + 1, 0);
  vector<int> st;
  for (int i = n - 1; i >= 0; i--) {
    while (!st.empty() && a[st.back()] <= a[i]) {
      st.pop_back();
    }
    int next = st.empty() ? n : st.back();
    g[next].push_back(i);
    st.push_back(i);
  }
  dfs(n);
  tmax.assign(4 * (n + 1), 0);
  tadd.assign(4 * (n + 1), 0);
  for (int i = 0; i < k - 1; i++) {
    add(0, 0, n + 1, tin[i], tout[i], +1);
  }
  for (int i = 0; i + k <= n; i++) {
    add(0, 0, n + 1, tin[i + k - 1], tout[i + k - 1], +1);
    cout << getmax(0) << " ";
    add(0, 0, n + 1, tin[i], tout[i], -1);
  }
  cout << "\n";
  return 0;
}
