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;
ifstream in;
ofstream out;
const long long kk = 1000;
const long long ml = kk * kk;
const long long mod = ml * kk + 7;
struct vertex {
  long max, push;
};
vector<vertex> t;
long n, i, j, s, k;
vector<long> m, las;
bool viv = false;
void read() {
  cin >> n >> k;
  for (i = 0; i < n; i++) {
    long a;
    cin >> a;
    m.push_back(a);
  }
}
void build() {
  s = 1;
  while (s < n) s <<= 1;
  t.resize(2 * s);
}
void prepare() {
  vector<long> st;
  for (long i = 0; i < n; i++) {
    while (st.size() && m[st.back()] < m[i]) st.pop_back();
    if (st.size())
      las.push_back(st.back());
    else
      las.push_back(-1);
    st.push_back(i);
  }
  build();
}
void upd(long v) {
  if (v >= s) return;
  long val = max(t[2 * v].max, t[2 * v + 1].max);
  t[v].max = max(t[v].max, val);
}
void push(long v) {
  if (v >= s) return;
  long add = t[v].push;
  t[v].push = 0;
  t[2 * v].max += add;
  t[2 * v + 1].max += add;
  t[2 * v].push += add;
  t[2 * v + 1].push += add;
}
void add(long l, long r, long v, long tl, long tr, long val) {
  if (r < tl || tr < l) return;
  push(v);
  if (l <= tl && tr <= r) {
    t[v].push += val;
    t[v].max += val;
    return;
  }
  long tm = tl + tr >> 1;
  add(l, r, 2 * v, tl, tm, val);
  add(l, r, 2 * v + 1, tm + 1, tr, val);
  upd(v);
}
long get(long l, long r, long v, long tl, long tr) {
  if (r < tl || tr < l) return 0;
  push(v);
  if (l <= tl && tr <= r) return t[v].max;
  long tm = tl + tr >> 1;
  long v1 = get(l, r, 2 * v, tl, tm);
  long v2 = get(l, r, 2 * v + 1, tm + 1, tr);
  return max(v1, v2);
}
void work(long pl) {
  long l = las[pl] + 1;
  long r = pl;
  add(l, r, 1, 0, s - 1, 1);
  if (pl >= k - 1) cout << get(pl - k + 1, pl, 1, 0, s - 1) << ' ';
}
void write() {
  if (!viv) return;
  cout << "Segment tree:" << endl;
  for (long i = 1; i < 2 * s; i++)
    cout << "{" << t[i].max << ' ' << t[i].push << "} ";
  cout << endl;
}
int main() {
  ios_base::sync_with_stdio(0);
  cin.tie(0);
  cout.tie(0);
  read();
  prepare();
  if (viv) {
    cout << "Better:" << endl;
    for (auto i : las) cout << i << ' ';
    cout << endl;
  }
  for (long i = 0; i < n; i++) work(i);
  return 0;
}
