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>
const long long MOD = 1e9 + 7;
const long long MAXN = 2e6 + 55;
using namespace std;
long long readInt() {
  bool minus1 = false;
  long long result = 0;
  char ch;
  ch = getchar();
  while (true) {
    if (ch == '-') break;
    if (ch >= '0' && ch <= '9') break;
    ch = getchar();
  }
  if (ch == '-')
    minus1 = true;
  else
    result = ch - '0';
  while (true) {
    ch = getchar();
    if (ch < '0' || ch > '9') break;
    result = result * 10 + (ch - '0');
  }
  if (minus1)
    return -result;
  else
    return result;
}
int timer = 0;
int a[MAXN];
int tin[MAXN];
int tout[MAXN];
vector<int> g[MAXN];
int used[MAXN];
void dfs(int v) {
  timer++;
  used[v] = 1;
  tin[v] = timer;
  for (int i : g[v]) {
    if (!used[i]) dfs(i);
  }
  tout[v] = timer;
}
long long t[MAXN * 4], to[MAXN * 4];
void Push(long long v) {
  if (to[v]) {
    t[v * 2] += to[v];
    t[v * 2 + 1] += to[v];
    to[v * 2] += to[v];
    to[v * 2 + 1] += to[v];
    to[v] = 0;
  }
}
void Upd(long long v, long long tl, long long tr, long long l, long long r,
         long long x) {
  Push(v);
  if (l > r) return;
  if (l == tl && r == tr) {
    t[v] += x;
    to[v] += x;
  } else {
    long long tm = (tl + tr) / 2;
    Upd(v * 2, tl, tm, l, min(r, tm), x);
    Upd(v * 2 + 1, tm + 1, tr, max(l, tm + 1), r, x);
    t[v] = max(t[v * 2], t[v * 2 + 1]);
  }
}
long long Get_Max(long long v, long long tl, long long tr, long long l,
                  long long r) {
  Push(v);
  if (l > r) return 0;
  if (l == tl && r == tr) {
    return t[v];
  } else {
    long long tm = (tl + tr) / 2;
    return max(Get_Max(v * 2, tl, tm, l, min(r, tm)),
               Get_Max(v * 2 + 1, tm + 1, tr, max(l, tm + 1), r));
  }
}
int main() {
  int n = readInt(), k = readInt();
  for (int i = 1; i <= n; i++) {
    a[i] = readInt();
  }
  vector<int> st;
  for (int i = n; i >= 1; i--) {
    while (!st.empty() && a[st.back()] <= a[i]) {
      st.pop_back();
    }
    int nxt = st.empty() ? (n + 1) : st.back();
    g[nxt].push_back(i);
    st.push_back(i);
  }
  dfs(n + 1);
  for (int i = 1; i < k; i++) {
    Upd(1, 1, n + 1, tin[i], tout[i], 1);
  }
  for (int i = 0; i < n - k + 1; i++) {
    Upd(1, 1, n + 1, tin[i + k], tout[i + k], 1);
    cout << t[1] << ' ';
    Upd(1, 1, n + 1, tin[i + 1], tout[i + 1], -1);
  }
  return 0;
}
