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>
#pragma GCC optimize("O2")
#pragma GCC optimize("unroll-loops")
using namespace std;
const long double eps = 1e-7;
const int inf = 1000000010;
const long long INF = 10000000000000010LL;
const int mod = 1000000007;
const int MAXN = 1000010, LOG = 20;
int n, m, k, u, v, x, y, t, a, b, ans;
int A[MAXN], R[MAXN];
int stt[MAXN], fnt[MAXN], timer;
int seg[MAXN << 2], lazy[MAXN << 2];
vector<int> G[MAXN];
void dfs(int node) {
  stt[node] = timer++;
  for (int v : G[node]) dfs(v);
  fnt[node] = timer;
}
void add_lazy(int id, int val) {
  seg[id] += val;
  lazy[id] += val;
}
void shift(int id) {
  if (!lazy[id]) return;
  add_lazy(id << 1, lazy[id]);
  add_lazy(id << 1 | 1, lazy[id]);
  lazy[id] = 0;
}
void Add(int id, int tl, int tr, int l, int r, int val) {
  if (r <= tl || tr <= l) return;
  if (l <= tl && tr <= r) {
    add_lazy(id, val);
    return;
  }
  shift(id);
  int mid = (tl + tr) >> 1;
  Add(id << 1, tl, mid, l, r, val);
  Add(id << 1 | 1, mid, tr, l, r, val);
  seg[id] = max(seg[id << 1], seg[id << 1 | 1]);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> A[i];
  for (int i = n; i; i--) {
    for (R[i] = i + 1; R[i] <= n && A[R[i]] <= A[i]; R[i] = R[R[i]])
      ;
    G[R[i]].push_back(i);
  }
  dfs(n + 1);
  for (int i = 1; i <= n; i++) {
    Add(1, 1, n + 1, stt[i], fnt[i], +1);
    if (k <= i) {
      Add(1, 1, n + 1, stt[i - k], stt[i - k] + 1, -inf);
      cout << seg[1] << ' ';
    }
  }
  return 0;
}
