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 maxn = 1000005;
const int unit = 450;
int n, m, a[maxn], b[maxn], l[maxn], r[maxn];
long long t[maxn << 2], lz[maxn << 2], tim;
vector<int> v[maxn];
void dfs(int x) {
  l[x] = ++tim;
  for (auto u : v[x]) dfs(u);
  r[x] = tim;
}
void update(int L, int R, int d, int l, int r, int rt) {
  if (L <= l && r <= R) {
    lz[rt] += 1ll * d;
    return;
  }
  int mid = l + r >> 1;
  if (L <= mid) update(L, R, d, l, mid, rt << 1);
  if (mid < R) update(L, R, d, mid + 1, r, rt << 1 | 1);
  t[rt] = max(t[((rt << 1) | 1)] + lz[((rt << 1) | 1)],
              t[(rt << 1)] + lz[(rt << 1)]);
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> m;
  for (int i = (1); i < (n + 1); i++) cin >> a[i];
  for (int i = n; i > 0; i--) {
    for (b[i] = i + 1; b[i] <= n && a[b[i]] <= a[i]; b[i] = b[b[i]])
      ;
    v[b[i]].push_back(i);
  }
  dfs(n + 1);
  for (int i = (1); i < (m + 1); i++) update(l[i], r[i], 1, 1, tim, 1);
  cout << t[1] + lz[1] << " ";
  for (int i = (m + 1); i < (n + 1); i++) {
    update(l[i], r[i], 1, 1, tim, 1);
    update(l[i - m], r[i - m], -n, 1, tim, 1);
    cout << t[1] + lz[1] << " ";
  }
  return 0;
}
