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 int N = 1000000;
const int oo = 0x3f3f3f3f;
namespace SEG {
const int SZ = N << 2;
int tag[SZ + 5], mx[SZ + 5];
void push_down(int u) {
  if (tag[u]) {
    mx[(u << 1)] += tag[u], tag[(u << 1)] += tag[u];
    mx[(u << 1 | 1)] += tag[u], tag[(u << 1 | 1)] += tag[u];
  }
  tag[u] = 0;
}
void add(int u, int l, int r, int x, int y, int v) {
  if (x <= l && r <= y) {
    mx[u] += v;
    tag[u] += v;
  } else {
    if (x <= ((l + r) >> 1)) add((u << 1), l, ((l + r) >> 1), x, y, v);
    if (((l + r) >> 1) < y) add((u << 1 | 1), ((l + r) >> 1) + 1, r, x, y, v);
    mx[u] = max(mx[(u << 1)], mx[(u << 1 | 1)]);
  }
}
int query(int u, int l, int r, int x, int y) {
  if (x > r || y < l) return -oo;
  if (x <= l && r <= y) return mx[u];
  push_down(u);
  return max(query((u << 1), l, ((l + r) >> 1), x, y),
             query((u << 1 | 1), ((l + r) >> 1) + 1, r, x, y));
}
}  // namespace SEG
int n, k;
int a[N + 5];
int stk[N + 5], bnd[N + 5], top;
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; ++i) {
    scanf("%d", a + i);
    bnd[i] = i;
    while (top > 0 && a[stk[top - 1]] < a[i]) {
      bnd[i] = bnd[stk[top - 1]];
      --top;
    }
    stk[top++] = i;
  }
  for (int i = 1; i <= n; ++i) {
    SEG::add(1, 1, n, bnd[i], i, +1);
    if (i - k + 1 > 0) {
      printf("%d ", SEG::query(1, 1, n, i - k + 1, i));
    }
  }
  return 0;
}
