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;
long long read() {
  long long x = 0, F = 1;
  char c = getchar();
  while (c < '0' || c > '9') {
    if (c == '-') F = -1;
    c = getchar();
  }
  while (c >= '0' && c <= '9') {
    x = x * 10 + c - '0';
    c = getchar();
  }
  return x * F;
}
int n, k, a[1000000 + 5], stk[1000000 + 5], tp;
int dfn[1000000 + 5], ot[1000000 + 5], ct;
vector<int> G[1000000 + 5];
struct Seg_tree {
  int mx[(1000000 << 2) + 5], tag[(1000000 << 2) + 5];
  void pushdown(int x) {
    if (tag[x]) {
      mx[(x << 1)] += tag[x], tag[(x << 1)] += tag[x];
      mx[(x << 1 | 1)] += tag[x], tag[(x << 1 | 1)] += tag[x];
      tag[x] = 0;
    }
  }
  void Insert(int x, int l, int r, int L, int R, int v) {
    if (r < L || R < l) return;
    if (L <= l && r <= R) {
      tag[x] += v, mx[x] += v;
      return;
    }
    pushdown(x);
    Insert((x << 1), l, (l + r >> 1), L, R, v),
        Insert((x << 1 | 1), (l + r >> 1) + 1, r, L, R, v);
    mx[x] = max(mx[(x << 1)], mx[(x << 1 | 1)]);
  }
} T;
void dfs(int x) {
  dfn[x] = ++ct;
  for (int i = 0; i < G[x].size(); i++) dfs(G[x][i]);
  ot[x] = ct;
}
int main() {
  n = read(), k = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  a[n + 1] = n + 1;
  for (int i = 1; i <= n + 1; i++) {
    while (tp && a[stk[tp]] < a[i]) G[i].push_back(stk[tp]), tp--;
    stk[++tp] = i;
  }
  dfs(n + 1);
  for (int i = 1; i <= k; i++) T.Insert(1, 1, n + 1, dfn[i], ot[i], 1);
  printf("%d ", T.mx[1]);
  for (int i = k + 1; i <= n; i++) {
    T.Insert(1, 1, n + 1, dfn[i - k], ot[i - k], -1);
    T.Insert(1, 1, n + 1, dfn[i], ot[i], 1);
    printf("%d ", T.mx[1]);
  }
}
