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 N = 1e6 + 10;
const int INF = 1e9;
struct SegmentTree {
  int st[4 * N], lp[4 * N];
  void Propagate(int k) {
    int v = lp[k];
    if (v == 0) return;
    lp[k] = 0;
    lp[k << 1] += v;
    lp[k << 1 | 1] += v;
    st[k << 1] += v;
    st[k << 1 | 1] += v;
  }
  void Assign(int k, int l, int r, int i, int v) {
    if (l > i || r < i) return;
    if (l == r) {
      st[k] = v;
      return;
    }
    Propagate(k);
    Assign(k << 1, l, ((l + r) >> 1), i, v);
    Assign(k << 1 | 1, ((l + r) >> 1) + 1, r, i, v);
    st[k] = max(st[k << 1], st[k << 1 | 1]);
  }
  void Update(int k, int l, int r, int i, int j, int v) {
    if (l > j || r < i) return;
    if (i <= l && r <= j) {
      st[k] += v;
      lp[k] += v;
      return;
    }
    Propagate(k);
    Update(k << 1, l, ((l + r) >> 1), i, j, v);
    Update(k << 1 | 1, ((l + r) >> 1) + 1, r, i, j, v);
    st[k] = max(st[k << 1], st[k << 1 | 1]);
  }
  int get(int k, int l, int r, int i) {
    if (l == r) return st[k];
    Propagate(k);
    if (i <= ((l + r) >> 1)) return get(k << 1, l, ((l + r) >> 1), i);
    return get(k << 1 | 1, ((l + r) >> 1) + 1, r, i);
  }
} ST;
int n, m;
int a[N], L[N], R[N], f[N];
void Init() {
  stack<int> ST;
  for (int i = 1; i <= n; ++i) {
    while (ST.size() && a[ST.top()] < a[i]) ST.pop();
    L[i] = (ST.size() == 0 ? 1 : ST.top() + 1);
    ST.push(i);
  }
  while (ST.size()) ST.pop();
  for (int i = n; i >= 1; --i) {
    while (ST.size() && a[ST.top()] <= a[i]) ST.pop();
    R[i] = (ST.size() == 0 ? n : ST.top() - 1);
    ST.push(i);
  }
  for (int i = n; i >= n - m + 1; --i) {
    int j = R[i];
    f[i] = (j >= n ? 1 : f[j + 1] + 1);
  }
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cin >> n >> m;
  for (int i = 1; i <= n; ++i) cin >> a[i];
  Init();
  for (int i = n - m + 1; i <= n; ++i) ST.Assign(1, 1, n, i, f[i]);
  vector<int> ans;
  for (int i = n - m + 1; i >= 1; --i) {
    ans.push_back(ST.st[1]);
    int r = i + m - 1;
    int l = L[r];
    if (l <= r - 1) ST.Update(1, 1, n, l, r - 1, -1);
    ST.Assign(1, 1, n, r, -INF);
    if (i - 1 >= 1) {
      int j = R[i - 1];
      f[i - 1] = (j + 1 >= r ? 1 : ST.get(1, 1, n, j + 1) + 1);
      ST.Assign(1, 1, n, i - 1, f[i - 1]);
    }
  }
  reverse(ans.begin(), ans.end());
  for (int v : ans) cout << v << ' ';
  cout << '\n';
  return 0;
}
