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 = 1000010;
int n, k, arr[N], idx[N], last[N], dfs_cnt = 0;
vector<int> g[N];
stack<int> st;
bool vis[N];
int seg[4 * N], lazy[4 * N];
void DFS(int node) {
  idx[node] = last[node] = dfs_cnt++;
  vis[node] = true;
  for (int i = 0; i < (int)g[node].size(); i++) {
    DFS(g[node][i]);
    last[node] = last[g[node][i]];
  }
}
inline void fix(int s, int e, int idx) {
  seg[idx] += lazy[idx];
  if (s != e) {
    lazy[(idx << 1)] += lazy[idx];
    lazy[(idx << 1) + 1] += lazy[idx];
  }
  lazy[idx] = 0;
}
int l, r, val;
int update(int s, int e, int idx) {
  fix(s, e, idx);
  if (s > r || e < l) return seg[idx];
  if (s >= l && e <= r) {
    lazy[idx] += val;
    fix(s, e, idx);
    return seg[idx];
  }
  return seg[idx] = max(update(s, (s + e) / 2, idx * 2),
                        update((s + e) / 2 + 1, e, idx * 2 + 1));
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 0; i < n; i++) {
    scanf("%d", &arr[i]);
    while ((int)st.size() > 0 && arr[i] > arr[st.top()]) {
      g[i].push_back(st.top());
      st.pop();
    }
    st.push(i);
  }
  for (int i = n - 1; i >= 0; i--) {
    if (!vis[i]) DFS(i);
  }
  int j = 0;
  for (j = 0; j < k; j++) {
    l = idx[j];
    r = last[j];
    val = 1;
    update(0, n - 1, 1);
  }
  j--;
  int ss;
  while (j < n) {
    fix(0, n - 1, 1);
    printf("%d ", seg[1]);
    ss = j - k + 1;
    l = idx[ss];
    r = idx[ss];
    val = -1000000010;
    update(0, n - 1, 1);
    j++;
    if (j == n) break;
    l = idx[j];
    r = last[j];
    val = 1;
    update(0, n - 1, 1);
  }
  puts("");
  return 0;
}
