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;
char buf[1 << 20], *p1, *p2;
inline unsigned int read() {
  unsigned int s = 0, f = 1;
  char ch = (p1 == p2 ? (p2 = buf + fread(p1 = buf, 1, 1 << 20, stdin),
                         p1 == p2 ? EOF : *p1++)
                      : *p1++);
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -f;
    ch = (p1 == p2 ? (p2 = buf + fread(p1 = buf, 1, 1 << 20, stdin),
                      p1 == p2 ? EOF : *p1++)
                   : *p1++);
  };
  while (ch >= '0' && ch <= '9') {
    s = (s << 1) + (s << 3) + ch - '0';
    ch = (p1 == p2 ? (p2 = buf + fread(p1 = buf, 1, 1 << 20, stdin),
                      p1 == p2 ? EOF : *p1++)
                   : *p1++);
  };
  return s * f;
}
const unsigned int maxn = 1e6 + 10;
unsigned int sta[maxn], top;
unsigned int nxt[maxn], las[maxn], val[maxn], a[maxn];
unsigned int tree[maxn << 2], lazy[maxn << 2];
void build(unsigned int rt, unsigned int l, unsigned int r) {
  if (l == r) return tree[rt] = val[l], void();
  build((rt << 1), l, ((l + r) >> 1));
  build((rt << 1 | 1), ((l + r) >> 1) + 1, r);
  tree[rt] = max(tree[(rt << 1)], tree[(rt << 1 | 1)]);
}
void update(unsigned int rt, unsigned int val) {
  lazy[rt] += val;
  tree[rt] += val;
  return;
}
void push_down(unsigned int rt) {
  if (!lazy[rt]) return;
  update((rt << 1), lazy[rt]);
  update((rt << 1 | 1), lazy[rt]);
  lazy[rt] = 0;
}
unsigned int ask(unsigned int rt, unsigned int l, unsigned int r,
                 unsigned int s, unsigned int t) {
  if (s <= l && t >= r) return tree[rt];
  push_down(rt);
  unsigned int Max = 0;
  if (s <= ((l + r) >> 1))
    Max = max(Max, ask((rt << 1), l, ((l + r) >> 1), s, t));
  if (t > ((l + r) >> 1))
    Max = max(Max, ask((rt << 1 | 1), ((l + r) >> 1) + 1, r, s, t));
  return Max;
}
void del(unsigned int rt, unsigned int l, unsigned int r, unsigned int pos) {
  if (l == r) return tree[rt] = 0, void();
  push_down(rt);
  if (pos <= ((l + r) >> 1))
    del((rt << 1), l, ((l + r) >> 1), pos);
  else
    del((rt << 1 | 1), ((l + r) >> 1) + 1, r, pos);
  tree[rt] = max(tree[(rt << 1)], tree[(rt << 1 | 1)]);
}
void add(unsigned int rt, unsigned int l, unsigned int r, unsigned int s,
         unsigned int t, unsigned int val) {
  if (s <= l && t >= r) return update(rt, val), void();
  push_down(rt);
  if (s <= ((l + r) >> 1)) add((rt << 1), l, ((l + r) >> 1), s, t, val);
  if (t > ((l + r) >> 1)) add((rt << 1 | 1), ((l + r) >> 1) + 1, r, s, t, val);
  tree[rt] = max(tree[(rt << 1)], tree[(rt << 1 | 1)]);
}
signed main() {
  unsigned int n = read(), k = read();
  for (unsigned int i = 1; i <= n; i++) a[i] = read();
  for (unsigned int i = k; i >= 1; i--) {
    while (top && a[sta[top]] <= a[i]) top--;
    nxt[i] = sta[top];
    sta[++top] = i;
  }
  for (unsigned int i = k; i >= 1; i--) val[i] = val[nxt[i]] + 1;
  top = 0;
  for (unsigned int i = 1; i <= n; i++) {
    while (top && a[sta[top]] < a[i]) top--;
    las[i] = sta[top];
    sta[++top] = i;
  }
  build(1, 1, n);
  printf("%d ", tree[1]);
  del(1, 1, n, 1);
  for (unsigned int i = 2; i + k - 1 <= n; i++) {
    unsigned int pos = las[i + k - 1] + 1;
    add(1, 1, n, max(i, pos), i + k - 1, 1);
    printf("%d ", tree[1]);
    del(1, 1, n, i);
  }
  puts("");
}
