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 tr[1000005 * 4], mark[1000005 * 4], dfn[1000005], deep[1000005], n, k,
    a[1000005], nx[1000005], sz, R[1000005], ans[1000005], cnt;
vector<int> G[1000005];
void dfs(int x) {
  dfn[x] = ++sz;
  for (auto u : G[x])
    if (!dfn[u]) {
      deep[u] = deep[x] + 1;
      dfs(u);
    }
  R[x] = sz;
}
void insert(int p, int l, int r, int x, int u) {
  if (x > r || l > x) return;
  if (l == r) {
    tr[p] += u;
    return;
  }
  if (mark[p]) {
    mark[p * 2] += mark[p];
    mark[p * 2 + 1] += mark[p];
    tr[p * 2] -= mark[p];
    tr[p * 2 + 1] -= mark[p];
    mark[p] = 0;
  }
  int mid = (l + r) / 2;
  insert(p * 2, l, mid, x, u);
  insert(p * 2 + 1, mid + 1, r, x, u);
  tr[p] = max(tr[p * 2], tr[p * 2 + 1]);
}
void del(int p, int l, int r, int x, int y) {
  if (x > r || l > y) return;
  if (x <= l && r <= y) {
    tr[p]--;
    mark[p]++;
    return;
  }
  if (mark[p]) {
    mark[p * 2] += mark[p];
    mark[p * 2 + 1] += mark[p];
    tr[p * 2] -= mark[p];
    tr[p * 2 + 1] -= mark[p];
    mark[p] = 0;
  }
  int mid = (l + r) / 2;
  del(p * 2, l, mid, x, y);
  del(p * 2 + 1, mid + 1, r, x, y);
  tr[p] = max(tr[p * 2], tr[p * 2 + 1]);
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  a[n + 1] = n + 1;
  nx[n] = n + 1;
  for (int i = n - 1; i >= 1; i--) {
    nx[i] = i + 1;
    while (a[nx[i]] <= a[i]) nx[i] = nx[nx[i]];
    G[nx[i]].push_back(i);
  }
  for (int i = n; i >= 1; i--)
    if (!dfn[i]) {
      deep[i] = 1;
      dfs(i);
    }
  for (int i = n; i >= n - k + 1; i--) insert(1, 1, n, dfn[i], deep[i]);
  ans[++cnt] = tr[1];
  for (int i = n - k; i >= 1; i--) {
    insert(1, 1, n, dfn[i], deep[i]);
    del(1, 1, n, dfn[i + k], R[i + k]);
    ans[++cnt] = tr[1];
  }
  for (int i = cnt; i >= 1; i--) printf("%d ", ans[i]);
}
