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>
#pragma comment(linker, "/STACK:1024000000,1024000000")
using namespace std;
const int inf = 0x3f3f3f3f;
const long long INF = 1e18;
template <typename T>
void read(T &x) {
  x = 0;
  int s = 1, c = getchar();
  for (; !isdigit(c); c = getchar())
    if (c == '-') s = -1;
  for (; isdigit(c); c = getchar()) x = x * 10 + c - 48;
  x *= s;
}
template <typename T>
void write(T x) {
  if (x < 0) x = -x, putchar('-');
  if (x > 9) write(x / 10);
  putchar(x % 10 + '0');
}
template <typename T>
void writeln(T x) {
  write(x);
  puts("");
}
const int maxn = 1e6 + 5;
int n, k, a[maxn], dfn[maxn], Time, size[maxn];
vector<int> adj[maxn];
class SegmentTree {
 public:
  struct Node {
    int l, r, maxx, tag;
  } t[maxn << 2];
  void Push_up(int p) { t[p].maxx = max(t[p << 1].maxx, t[p << 1 | 1].maxx); }
  void Push_down(int p) {
    if (t[p].tag) {
      t[p << 1].maxx += t[p].tag, t[p << 1 | 1].maxx += t[p].tag;
      t[p << 1].tag += t[p].tag, t[p << 1 | 1].tag += t[p].tag;
      t[p].tag = 0;
    }
  }
  void Build(int l, int r, int p) {
    t[p].l = l, t[p].r = r;
    if (l == r) return;
    int mid = (l + r) >> 1;
    Build(l, mid, p << 1);
    Build(mid + 1, r, p << 1 | 1);
  }
  void Modify(int l, int r, int p, int k) {
    if (l <= t[p].l && t[p].r <= r) {
      t[p].maxx += k, t[p].tag += k;
      return;
    }
    Push_down(p);
    int mid = (t[p].l + t[p].r) >> 1;
    if (l <= mid) Modify(l, r, p << 1, k);
    if (mid < r) Modify(l, r, p << 1 | 1, k);
    Push_up(p);
  }
} T;
void dfs(int fa) {
  dfn[fa] = ++Time;
  size[fa] = 1;
  for (auto i : adj[fa]) {
    dfs(i);
    size[fa] += size[i];
  }
}
void Pre() {
  stack<int> st;
  for (int i = n; i >= 1; i--) {
    while (!st.empty() && a[st.top()] <= a[i]) st.pop();
    int fa = st.empty() ? n + 1 : st.top();
    adj[fa].push_back(i);
    st.push(i);
  }
  dfs(n + 1);
}
void Solve() {
  T.Build(1, n + 1, 1);
  for (int i = 1; i <= k - 1; i++) T.Modify(dfn[i], dfn[i] + size[i] - 1, 1, 1);
  for (int i = 1; i + k - 1 <= n; i++) {
    T.Modify(dfn[i + k - 1], dfn[i + k - 1] + size[i + k - 1] - 1, 1, 1);
    printf("%d ", T.t[1].maxx);
    T.Modify(dfn[i], dfn[i] + size[i] - 1, 1, -1);
  }
}
int main() {
  read(n), read(k);
  for (int i = 1; i <= n; i++) read(a[i]);
  Pre();
  Solve();
  return 0;
}
