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 s[1000005 << 2], tag[1000005 << 2];
inline void upd(int rt, int v) { s[rt] += v, tag[rt] += v; }
inline void PushUp(int rt) { s[rt] = max(s[rt << 1], s[rt << 1 | 1]); }
inline void PushDown(int rt) {
  if (tag[rt]) upd(rt << 1, tag[rt]), upd(rt << 1 | 1, tag[rt]), tag[rt] = 0;
}
void Update(int L, int R, int l, int r, int rt) {
  if (L <= l && r <= R) return upd(rt, 1);
  PushDown(rt);
  int m = (l + r) >> 1;
  if (L <= m) Update(L, R, l, m, rt << 1);
  if (m < R) Update(L, R, m + 1, r, rt << 1 | 1);
  PushUp(rt);
}
int query(int L, int R, int l, int r, int rt) {
  if (L <= l && r <= R) return s[rt];
  PushDown(rt);
  int m = (l + r) >> 1, ret = 0;
  if (L <= m) ret = query(L, R, l, m, rt << 1);
  if (m < R) ret = max(ret, query(L, R, m + 1, r, rt << 1 | 1));
  return ret;
}
int sta[1000005], top, pre[1000005], a[1000005], n, k;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]);
  for (int i = n; i; i--) {
    while (top && a[sta[top]] <= a[i]) pre[sta[top]] = i, top--;
    sta[++top] = i;
  }
  for (int i = 1; i <= n; i++) {
    Update(pre[i] + 1, i, 1, n, 1);
    if (i >= k) printf("%d ", query(i - k + 1, i, 1, n, 1));
  }
  puts("");
}
