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 + 10;
int seg[4 * maxn], lazy[4 * maxn];
void propagate(int, int, int);
int get(int id, int L, int R, int l, int r) {
  if (L == l and R == r) return seg[id];
  propagate(id, L, R);
  int mid = (L + R) >> 1, ret = 0;
  if (l < mid) ret = max(ret, get(2 * id + 0, L, mid, l, min(mid, r)));
  if (mid < r) ret = max(ret, get(2 * id + 1, mid, R, max(l, mid), r));
  return ret;
}
void add(int id, int L, int R, int l, int r, int val = 1) {
  if (L == l and R == r) {
    seg[id] += val;
    lazy[id] += val;
    return;
  }
  propagate(id, L, R);
  int mid = (L + R) >> 1;
  if (l < mid) add(2 * id + 0, L, mid, l, min(mid, r));
  if (mid < r) add(2 * id + 1, mid, R, max(l, mid), r);
  seg[id] = max(seg[2 * id + 0], seg[2 * id + 1]);
}
void propagate(int id, int L, int R) {
  if (lazy[id] == 0) return;
  int mid = (L + R) >> 1;
  add(2 * id + 0, L, mid, L, mid, lazy[id]);
  add(2 * id + 1, mid, R, mid, R, lazy[id]);
  lazy[id] = 0;
}
int a[maxn], pre[maxn];
int main() {
  ios_base::sync_with_stdio(false);
  int n, k;
  cin >> n >> k;
  for (int i = 0; i < n; i++) cin >> a[i];
  a[n] = n + 1;
  stack<int> st;
  st.push(n);
  for (int i = 0; i < n; i++) {
    while (a[st.top()] < a[i]) st.pop();
    pre[i] = st.top();
    if (pre[i] == n) pre[i] = -1;
    st.push(i);
  }
  int ptr = 0;
  for (int i = 0; i < n - k + 1; i++) {
    while (ptr - i < k) {
      add(1, 0, n, pre[ptr] + 1, ptr + 1);
      ptr++;
    }
    cout << get(1, 0, n, i, i + k) << " ";
  }
}
