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 = 1e6 + 10;
int f[N], a[N], tp[N], tg[N << 2], s[N << 2], ans[N], n, k, sta[N], top, p[N];
void add(int k, int z) {
  s[k] += z;
  tg[k] += z;
}
void push_d(int k) {
  if (tg[k] == 0) return;
  add(k << 1, tg[k]);
  add(k << 1 | 1, tg[k]);
  tg[k] = 0;
}
void push_up(int k) { s[k] = max(s[k << 1], s[k << 1 | 1]); }
void modify(int k, int l, int r, int x, int y, int z) {
  if (x <= l && r <= y) return add(k, z);
  int mid = l + r >> 1;
  push_d(k);
  if (x <= mid) modify(k << 1, l, mid, x, y, z);
  if (mid < y) modify(k << 1 | 1, mid + 1, r, x, y, z);
  push_up(k);
  return;
}
int query(int k, int l, int r, int x, int y) {
  if (x <= l && r <= y) return s[k];
  int mid = l + r >> 1, tp = 0;
  push_d(k);
  if (x <= mid) tp = query(k << 1, l, mid, x, y);
  if (mid < y) tp = max(tp, query(k << 1 | 1, mid + 1, r, x, y));
  push_up(k);
  return tp;
}
signed main() {
  ios::sync_with_stdio(false);
  cin.tie(0);
  cin >> n >> k;
  for (register int i = (1); i <= (n); ++i) cin >> a[i];
  for (register int i = (1); i <= (n); ++i) {
    while (top && a[sta[top]] < a[i]) top--;
    p[i] = sta[top] + 1;
    sta[++top] = i;
  }
  top = 0;
  for (register int i = (n); i >= (1); --i) {
    while (top && a[sta[top]] <= a[i]) top--;
    f[i] = f[sta[top]] + 1;
    sta[++top] = i;
    modify(1, 1, n, i, i, f[i]);
    if (i + k <= n) modify(1, 1, n, p[i + k], i + k, -1);
    if (i + k - 1 <= n) ans[i] = query(1, 1, n, i, i + k - 1);
  }
  for (register int i = (1); i <= (n - k + 1); ++i) cout << ans[i] << ' ';
  cout << '\n';
  return 0;
}
