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;
int st[1000007];
int top;
int s[1000007], t[1000007];
int mx[4000007];
int sum[4000007];
int head[1000007], to[2000007], nex[2000007];
int n, k;
int a[10000077];
int dfn;
int tot;
void pushup(int rt) { mx[rt] = max(mx[rt << 1], mx[rt << 1 | 1]); }
void pushdown(int rt) {
  if (sum[rt]) {
    sum[rt << 1] += sum[rt];
    sum[rt << 1 | 1] += sum[rt];
    mx[rt << 1] += sum[rt];
    mx[rt << 1 | 1] += sum[rt];
    sum[rt] = 0;
  }
}
void change(int rt, int l, int r, int L, int R, int x) {
  if (L <= l && r <= R) {
    sum[rt] += x;
    mx[rt] += x;
    return;
  }
  pushdown(rt);
  int mid = (l + r) >> 1;
  if (L <= mid) change(rt << 1, l, mid, L, R, x);
  if (R > mid) change(rt << 1 | 1, mid + 1, r, L, R, x);
  pushup(rt);
}
void add(int x, int y) {
  nex[++tot] = head[x];
  head[x] = tot;
  to[tot] = y;
}
void dfs(int x) {
  s[x] = ++dfn;
  for (int i = head[x]; i; i = nex[i]) dfs(to[i]);
  t[x] = dfn;
}
int main() {
  scanf("%d%d", &n, &k);
  for (int i = 1; i <= n; i++) {
    scanf("%d", &a[i]);
    while (top && a[st[top]] < a[i]) {
      add(i, st[top]);
      top--;
    }
    st[++top] = i;
  }
  while (top) {
    add(n + 1, st[top]);
    top--;
  }
  dfs(n + 1);
  for (int i = 1; i <= k; i++) change(1, 1, n + 1, s[i], t[i], 1);
  printf("%d ", mx[1]);
  for (int i = k + 1; i <= n; i++) {
    change(1, 1, n + 1, s[i], t[i], 1);
    change(1, 1, n + 1, s[i - k], t[i - k], -1);
    printf("%d ", mx[1]);
  }
}
