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 = 1000050;
const int M = 2 * N;
int lid[N], rid[N], tid;
vector<int> E[N];
void DFS(int u) {
  lid[u] = ++tid;
  for (int v : E[u]) DFS(v);
  rid[u] = tid;
}
int ls[M], rs[M], tsz, root, mx[M], lzy[M];
void Set(int &c, int ss, int se, int qs, int qe, int f) {
  if (qs > qe || qs > se || ss > qe) return;
  if (!c) c = ++tsz;
  if (qs <= ss && qe >= se) {
    mx[c] += f;
    lzy[c] += f;
    return;
  }
  int mid = ss + se >> 1;
  Set(ls[c], ss, mid, qs, qe, f);
  Set(rs[c], mid + 1, se, qs, qe, f);
  mx[c] = max(mx[ls[c]], mx[rs[c]]) + lzy[c];
}
int a[N], S[N], c;
int main() {
  int n, k, i;
  scanf("%i %i", &n, &k);
  for (i = 1; i <= n; i++) scanf("%i", &a[i]);
  for (i = n; i >= 1; i--) {
    while (c && a[S[c]] <= a[i]) c--;
    E[S[c]].push_back(i);
    S[++c] = i;
  }
  DFS(0);
  for (i = 1; i < k; i++) Set(root, 1, tid, lid[i], rid[i], 1);
  for (i = k; i <= n; i++) {
    Set(root, 1, tid, lid[i], rid[i], 1);
    if (i > k) Set(root, 1, tid, lid[i - k], rid[i - k], -1);
    printf("%i ", mx[root]);
  }
  return 0;
}
