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 = 1e6 + 10;
const int mod = 998244353;
const int inf = 0x3f3f3f3f;
int n, k, tim;
int a[N], nex[N], in[N], out[N];
vector<int> son[N];
template <typename T>
void read(T &x) {
  int f = 0;
  char c = getchar();
  while (c < '0' || c > '9') f |= (c == '-'), c = getchar();
  for (x = 0; c >= '0' && c <= '9'; c = getchar())
    x = (x << 3) + (x << 1) + c - '0';
  if (f) x = -x;
}
namespace BIT {
int tr[N];
void init() { memset(tr, 0x3f, sizeof tr); }
void upd(int x, int v) {
  for (int i = x; i; i -= i & -i) {
    tr[i] = min(tr[i], v);
  }
}
int query(int x) {
  int ans = inf;
  for (int i = x; i < N; i += i & -i) {
    ans = min(ans, tr[i]);
  }
  return ans;
}
}  // namespace BIT
namespace SEG {
int tr[N << 2], tag[N << 2];
void pushdown(int x) {
  tr[x << 1] += tag[x];
  tr[x << 1 | 1] += tag[x];
  tag[x << 1] += tag[x];
  tag[x << 1 | 1] += tag[x];
  tag[x] = 0;
}
void update(int x, int l, int r, int ql, int qr, int v) {
  if (ql <= l && r <= qr) {
    tr[x] += v;
    tag[x] += v;
    return;
  }
  pushdown(x);
  int mid = (l + r) >> 1;
  if (mid >= ql) {
    update(x << 1, l, mid, ql, qr, v);
  }
  if (mid < qr) {
    update(x << 1 | 1, mid + 1, r, ql, qr, v);
  }
  tr[x] = max(tr[x << 1], tr[x << 1 | 1]);
}
}  // namespace SEG
void dfs(int x) {
  in[x] = out[x] = ++tim;
  for (auto i : son[x]) {
    dfs(i);
    out[x] = max(out[x], out[i]);
  }
}
int main() {
  read(n);
  read(k);
  for (int i = 1; i <= n; ++i) read(a[i]);
  BIT::init();
  BIT::upd(n + 1, n + 1);
  for (int i = n; i >= 1; --i) {
    nex[i] = BIT::query(a[i]);
    if (a[i] > 1) BIT::upd(a[i] - 1, i);
  }
  for (int i = 1; i <= n; ++i) {
    son[nex[i]].push_back(i);
  }
  dfs(n + 1);
  for (int i = 1; i <= k; ++i) {
    SEG::update(1, 1, n + 1, in[i], out[i], 1);
  }
  printf("%d ", SEG::tr[1]);
  for (int i = k + 1; i <= n; ++i) {
    SEG::update(1, 1, n + 1, in[i - k], in[i - k], -inf);
    SEG::update(1, 1, n + 1, in[i], out[i], 1);
    printf("%d ", SEG::tr[1]);
  }
  puts("");
  return 0;
}
