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 = 1e6 + 5;
int n, k;
int maxv[4 * maxn];
int addv[4 * maxn];
int a[maxn];
int L[maxn];
void pushup(int o) { maxv[o] = max(maxv[o * 2], maxv[o * 2 + 1]); }
void pushdown(int o, int L, int R) {
  if (addv[o]) {
    addv[o * 2] += addv[o];
    addv[o * 2 + 1] += addv[o];
    maxv[o * 2] += addv[o];
    maxv[o * 2 + 1] += addv[o];
    addv[o] = 0;
  }
}
void update(int o, int L, int R, int ql, int qr, int v) {
  if (ql <= L && R <= qr) {
    addv[o] += v;
    maxv[o] += v;
    return;
  }
  pushdown(o, L, R);
  int M = (L + R) >> 1;
  if (ql <= M) update(o * 2, L, M, ql, qr, v);
  if (qr > M) update(o * 2 + 1, M + 1, R, ql, qr, v);
  pushup(o);
}
int query(int o, int L, int R, int ql, int qr) {
  if (ql <= L && R <= qr) {
    return maxv[o];
  }
  pushdown(o, L, R);
  int ret = 0;
  int M = (L + R) >> 1;
  if (ql <= M) ret = max(ret, query(o * 2, L, M, ql, qr));
  if (qr > M) ret = max(ret, query(o * 2 + 1, M + 1, R, ql, qr));
  pushup(o);
  return ret;
}
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  a[0] = 1e7;
  L[1] = 0;
  for (int i = 2; i <= n; i++) {
    int j = i - 1;
    while (a[i] > a[j]) j = L[j];
    L[i] = j;
  }
  for (int i = 1; i < k; i++) update(1, 1, n, L[i] + 1, i, 1);
  for (int i = 1, j = k; j <= n; i++, j++) {
    update(1, 1, n, L[j] + 1, j, 1);
    cout << query(1, 1, n, i, j) << " ";
  }
  return 0;
}
