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 f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
inline long long readll() {
  long long f = 1, x = 0;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (isdigit(ch)) {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int MAXN = 1e6 + 6;
int n, k, a[MAXN], pre[MAXN], sta[MAXN], t;
struct SegmentTree {
  int mx[MAXN << 2], tag[MAXN << 2];
  void push_down(int p) {
    if (tag[p]) {
      mx[p << 1] += tag[p];
      mx[p << 1 | 1] += tag[p];
      tag[p << 1] += tag[p];
      tag[p << 1 | 1] += tag[p];
      tag[p] = 0;
    }
  }
  void push_up(int p) { mx[p] = max(mx[p << 1], mx[p << 1 | 1]); }
  void modify(int p, int l, int r, int ql, int qr) {
    if (ql <= l && qr >= r) {
      mx[p]++;
      tag[p]++;
      return;
    }
    push_down(p);
    int mid = (l + r) >> 1;
    if (ql <= mid) modify(p << 1, l, mid, ql, qr);
    if (qr > mid) modify(p << 1 | 1, mid + 1, r, ql, qr);
    push_up(p);
  }
  int query(int p, int l, int r, int ql, int qr) {
    if (ql <= l && qr >= r) return mx[p];
    push_down(p);
    int mid = (l + r) >> 1, res = 0;
    if (ql <= mid) res = query(p << 1, l, mid, ql, qr);
    if (qr > mid) res = max(res, query(p << 1 | 1, mid + 1, r, ql, qr));
    push_up(p);
    return res;
  }
  SegmentTree() {}
} T;
int main() {
  n = read();
  k = read();
  for (int i = 1; i <= n; ++i) {
    a[i] = read();
    while (t && a[sta[t]] < a[i]) --t;
    pre[i] = sta[t];
    sta[++t] = i;
  }
  for (int i = 1; i <= n; ++i) {
    T.modify(1, 1, n, pre[i] + 1, i);
    if (i >= k) {
      printf("%d ", T.query(1, 1, n, i - k + 1, i));
    }
  }
  return 0;
}
