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 double pi = acos(-1);
const double eps = 1e-9;
const int mod = 1e9 + 7;
int n, k, a[1000005], nxt[1000005];
vector<int> g[1000005];
int td[1000005], tf[1000005], v, lev[1000005];
bool di[1000005];
int lca[1000005][25];
void dfs(int nod) {
  td[nod] = tf[nod] = ++v;
  for (int i = 1; i <= 20; i++) lca[nod][i] = lca[lca[nod][i - 1]][i - 1];
  for (int newn : g[nod]) {
    lev[newn] = lev[nod] + 1;
    lca[newn][0] = nod;
    dfs(newn);
    tf[nod] = tf[newn];
  }
}
int t[1000005 * 4];
void update(int ini, int fin, int lv, int pos, int v) {
  if (ini == fin) {
    t[lv] = v;
    return;
  }
  int piv = (ini + fin) >> 1;
  if (pos <= piv)
    update(ini, piv, lv * 2, pos, v);
  else
    update(piv + 1, fin, lv * 2 + 1, pos, v);
  t[lv] = max(t[lv * 2], t[lv * 2 + 1]);
}
int query(int ini, int fin, int lv, int a, int b) {
  if (a > fin || b < ini) return 0;
  if (a <= ini && b >= fin) return t[lv];
  int piv = (ini + fin) >> 1;
  return max(query(ini, piv, lv * 2, a, b),
             query(piv + 1, fin, lv * 2 + 1, a, b));
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) cin >> a[i];
  a[n + 1] = 1 << 30;
  for (int i = n; i >= 1; i--) {
    nxt[i] = i + 1;
    while (a[nxt[i]] <= a[i]) nxt[i] = nxt[nxt[i]];
    if (nxt[i] != n + 1) {
      g[nxt[i]].push_back(i);
      di[i] = true;
    }
  }
  for (int i = 1; i <= n; i++)
    if (!di[i]) {
      lev[i] = 1;
      dfs(i);
    }
  multiset<int> m;
  vector<int> s(n + 1);
  auto agrega = [&](int nod, int l, int r) {
    int val = 0;
    update(1, n, 1, td[nod], lev[nod]);
    for (int newn : g[nod]) {
      if (newn > r || newn < l) continue;
      m.erase(m.find(s[newn]));
      val = max(val, s[newn]);
    }
    s[nod] = val + 1;
    m.insert(s[nod]);
  };
  auto find_root = [&](int nod, int l, int r) {
    int root = nod;
    for (int i = 20; i >= 0; i--)
      if (lca[root][i] && lca[root][i] <= r) root = lca[root][i];
    return root;
  };
  auto elimina = [&](int nod, int l, int r) {
    update(1, n, 1, td[nod], 0);
    int root = find_root(nod, l, r);
    m.erase(m.find(s[root]));
    if (nod == root) return;
    s[root] = query(1, n, 1, td[root], tf[root]) - lev[root] + 1;
    m.insert(s[root]);
  };
  for (int i = 1; i <= n; i++) {
    if (i > k) elimina(i - k, i - k, i - 1);
    agrega(i, max(1, i - k + 1), i);
    if (i >= k) cout << *m.rbegin() << " \n"[i == n];
  }
  return 0;
}
