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;
inline int read() {
  int w = 1, s = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') w = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    s = s * 10 + ch - '0';
    ch = getchar();
  }
  return w * s;
}
struct Segment_Tree {
  int Max[4000010], tag[4000010];
  inline void Init() {
    memset(Max, 0, sizeof(Max));
    memset(tag, 0, sizeof(tag));
  }
  inline void Push(int x, int d) {
    Max[x] += d;
    tag[x] += d;
    return;
  }
  inline void Pushdown(int now) {
    if (!tag[now]) return;
    Push(now << 1, tag[now]);
    Push(now << 1 | 1, tag[now]);
    tag[now] = 0;
  }
  inline void Modify(int now, int l, int r, int x, int y, int d) {
    if (x <= l && r <= y) {
      Push(now, d);
      return;
    }
    int mid = (l + r) >> 1;
    Pushdown(now);
    if (x <= mid) Modify(now << 1, l, mid, x, y, d);
    if (y > mid) Modify(now << 1 | 1, mid + 1, r, x, y, d);
    Max[now] = max(Max[now << 1], Max[now << 1 | 1]);
  }
  inline int Query(int now, int l, int r, int x, int y) {
    if (x <= l && r <= y) return Max[now];
    int mid = (l + r) >> 1;
    Pushdown(now);
    int res = 0;
    if (x <= mid) res = Query(now << 1, l, mid, x, y);
    if (y > mid) res = max(res, Query(now << 1 | 1, mid + 1, r, x, y));
    Max[now] = max(Max[now << 1], Max[now << 1 | 1]);
    return res;
  }
} t;
int n, k, A[1000010], L[1010010], Sta[1000100];
int main() {
  n = read(), k = read();
  for (register int i = 1; i <= n; ++i) A[i] = read();
  int top = 0;
  t.Init();
  for (register int i = 1; i <= n; ++i) {
    while (top && A[i] > A[Sta[top]]) top--;
    L[i] = Sta[top];
    Sta[++top] = i;
  }
  for (register int i = 1; i <= n; ++i) {
    t.Modify(1, 1, n, L[i] + 1, i, 1);
    if (i >= k) cout << t.Query(1, 1, n, i - k + 1, i) << " ";
  }
  return 0;
}
