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, s, c, a[1000010], d[1000010], n1[1000010], n2[1000010], f1[1000010],
    f2[1000010], t[1000010];
bool v[1000010];
int main() {
  scanf("%d%d", &n, &s);
  if (s == 1) {
    for (int i = (1); i <= (n); ++i) printf("1 ");
    return 0;
  }
  for (int i = (1); i <= (n); ++i) scanf("%d", &a[i]);
  for (int i = n; i; --i) {
    while (c && d[c] <= a[i]) --c;
    d[++c] = a[i];
    a[i] = c;
    t[i] = i;
  }
  for (int i = (1); i <= (n); ++i) {
    int x = i - 1;
    for (; x && (a[x] > a[i] || a[t[x]] - a[x] <= a[t[i]] - a[i]); x = f2[x]) {
      int y = x;
      for (; y && a[t[i]] >= a[y]; y = f1[y]) v[y] = 1;
      if (y) {
        n1[y] = t[i];
        f1[t[i]] = y;
        t[i] = t[x];
      }
    }
    if (x)
      n2[x] = i, f2[i] = x;
    else
      c = i;
    if (i >= s) {
      printf("%d ", a[t[c]] - a[c] + 1);
      if (!v[i - s + 1]) {
        v[i - s + 1] = 1;
        t[c] = n1[i - s + 1];
        f1[n1[i - s + 1]] = 0;
        if (n2[c] && a[t[c]] - a[c] <= a[t[n2[c]]] - a[n2[c]]) {
          for (int j = i - s + 1; j; j = n1[j]) v[j] = 1;
          f2[n2[c]] = 0;
          c = n2[c];
        }
      }
    }
  }
}
