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 = 1000003;
int n, k, p[N], stk[N], top, head[N], to[N], nxt[N], dfn[N], siz[N], tim;
inline void add(int a, int b) {
  static int cnt = 0;
  to[++cnt] = b;
  nxt[cnt] = head[a];
  head[a] = cnt;
}
inline void dfs(int x) {
  dfn[x] = ++tim;
  siz[x] = 1;
  for (register int i = head[x]; i; i = nxt[i])
    dfs(to[i]), siz[x] += siz[to[i]];
}
int seg[N << 2], lazy[N << 2];
inline void pushdown(int x) {
  if (lazy[x]) {
    seg[x << 1] += lazy[x];
    seg[x << 1 | 1] += lazy[x];
    lazy[x << 1] += lazy[x];
    lazy[x << 1 | 1] += lazy[x];
    lazy[x] = 0;
  }
}
inline void pushup(int x) { seg[x] = max(seg[x << 1], seg[x << 1 | 1]); }
inline void change(int x, int L, int R, int l, int r, int v) {
  if (l <= L && R <= r) {
    seg[x] += v;
    lazy[x] += v;
    return;
  }
  int mid = L + R >> 1;
  pushdown(x);
  if (l <= mid) change(x << 1, L, mid, l, r, v);
  if (mid < r) change(x << 1 | 1, mid + 1, R, l, r, v);
  pushup(x);
}
int main() {
  scanf("%d%d", &n, &k);
  for (register int i = 1; i <= n; i++) scanf("%d", p + i);
  for (register int i = 1; i <= n; i++) {
    while (top && p[stk[top]] < p[i]) {
      add(i, stk[top]);
      --top;
    }
    stk[++top] = i;
  }
  while (top) add(n + 1, stk[top]), --top;
  dfs(n + 1);
  for (register int i = 1; i <= k; i++)
    change(1, 1, n + 1, dfn[i], dfn[i] + siz[i] - 1, 1);
  printf("%d", seg[1]);
  for (register int i = k + 1; i <= n; i++) {
    change(1, 1, n + 1, dfn[i], dfn[i] + siz[i] - 1, 1);
    change(1, 1, n + 1, dfn[i - k], dfn[i - k] + siz[i - k] - 1, -1);
    printf(" %d", seg[1]);
  }
}
