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;
unsigned int read() {
  unsigned int rt = 0;
  char c = getchar();
  while (c < '0' || c > '9') c = getchar();
  while (c >= '0' && c <= '9') {
    rt = rt * 10 + c - '0';
    c = getchar();
  }
  return rt;
}
struct Edge {
  unsigned int to, next;
} ed[1000005 * 2];
unsigned int head[1000005], cnt;
void add(int a, int b) {
  ed[++cnt].to = b;
  ed[cnt].next = head[a];
  head[a] = cnt;
}
unsigned int sta[1000005], a[1000005], size[1000005];
unsigned int n, k, top;
void init() {
  a[++n] = -1;
  sta[++top] = 1;
  size[1] = 1;
  for (int i = 2; i <= n; i++) {
    size[i] = 1;
    while (a[sta[top]] < a[i] && top) {
      add(i, sta[top]);
      size[i] += size[sta[top--]];
    }
    sta[++top] = i;
  }
}
unsigned int beg[1000005], last[1000005], dfs;
stack<int> q;
void fuckldy() {
  q.push(n);
  while (!q.empty()) {
    int x = q.top();
    q.pop();
    beg[x] = ++dfs;
    for (int i = head[x]; i; i = ed[i].next) q.push(ed[i].to);
  }
  for (int i = 1; i <= n; i++) last[i] = beg[i] + size[i] - 1;
}
struct node {
  int flag, maxx;
} nd[1000005 * 4];
void pushdown(int x) {
  nd[x << 1].maxx += nd[x].flag;
  nd[x << 1 | 1].maxx += nd[x].flag;
  nd[x << 1].flag += nd[x].flag;
  nd[x << 1 | 1].flag += nd[x].flag;
  nd[x].flag = 0;
}
void change(int l, int r, int x, int L, int R, int val) {
  if (l >= L && r <= R) {
    nd[x].flag += val;
    nd[x].maxx += val;
    return;
  }
  pushdown(x);
  int mid = l + r >> 1;
  if (L <= mid) change(l, mid, x << 1, L, R, val);
  if (R > mid) change(mid + 1, r, x << 1 | 1, L, R, val);
  nd[x].maxx = max(nd[x << 1].maxx, nd[x << 1 | 1].maxx);
}
int main() {
  n = read(), k = read();
  for (int i = 1; i <= n; i++) a[i] = read();
  init();
  fuckldy();
  for (int i = 1; i <= k; i++) change(1, n, 1, beg[i], last[i], 1);
  printf("%u ", nd[1].maxx);
  for (int i = k + 1, j = 1; i < n; i++, j++) {
    change(1, n, 1, beg[i], last[i], 1);
    change(1, n, 1, beg[j], last[j], -1);
    printf("%u ", nd[1].maxx);
  }
  return 0;
}
