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 M = 1e6 + 5;
int sta[M], tp, nxt[M], siz[M], head[M], cnt, ID[M], ord, w[M << 2],
    lazy[M << 2];
long long n, k, a[M];
stack<int> S;
long long read() {
  long long x = 0, f = 1;
  char ch = getchar();
  while (ch < '0' || ch > '9') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while ('0' <= ch && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return f * x;
}
struct edge {
  int v, next;
} e[M];
void add(int u, int v) {
  siz[u] += siz[v];
  e[++cnt].v = v;
  e[cnt].next = head[u];
  head[u] = cnt;
}
void pushup(int rt) { w[rt] = max(w[rt << 1], w[rt << 1 | 1]); }
void pushdown(int rt) {
  if (!lazy[rt]) return;
  int l = rt << 1, r = rt << 1 | 1;
  w[l] += lazy[rt];
  w[r] += lazy[rt];
  lazy[l] += lazy[rt];
  lazy[r] += lazy[rt];
  lazy[rt] = 0;
}
void update(int L, int R, int val, int l, int r, int rt) {
  if (L <= l && r <= R) {
    w[rt] += val;
    lazy[rt] += val;
    return;
  }
  pushdown(rt);
  int mid = (l + r) >> 1;
  if (L <= mid) update(L, R, val, l, mid, rt << 1);
  if (R > mid) update(L, R, val, mid + 1, r, rt << 1 | 1);
  pushup(rt);
}
int main() {
  n = read();
  k = read();
  for (int i = 1; i <= n; i++) a[i] = read(), siz[i] = 1;
  for (int i = 1; i <= n; i++) {
    while (a[i] > a[sta[tp]] && tp) nxt[sta[tp]] = i, add(i, sta[tp]), tp--;
    sta[++tp] = i;
  }
  while (tp) nxt[sta[tp]] = n + 1, add(n + 1, sta[tp]), tp--;
  S.push(++n);
  while (!S.empty()) {
    int s = S.top();
    S.pop();
    ID[s] = ++ord;
    for (int i = head[s]; i != 0; i = e[i].next) S.push(e[i].v);
  }
  for (int i = 1; i <= k; i++) update(ID[i], ID[i] + siz[i] - 1, 1, 1, n, 1);
  printf("%d ", w[1]);
  for (int i = k + 1; i < n; i++) {
    update(ID[i], ID[i] + siz[i] - 1, 1, 1, n, 1);
    update(ID[i - k], ID[i - k] + siz[i - k] - 1, -1, 1, n, 1);
    printf("%d ", w[1]);
  }
  return 0;
}
