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;
struct Node {
  int max;
  int lazyAdd;
};
int n, k;
int sequence[1000000];
int dpNext[1000000];
vector<int> rootIndices;
vector<vector<int>> edges;
int rangeStarts[1000000];
int rangeEnds[1000000];
int nextN = 0;
vector<Node> rt;
void topologicalSort(int node) {
  rangeStarts[node] = nextN;
  nextN++;
  for (int nextNode : edges[node]) {
    topologicalSort(nextNode);
  }
  rangeEnds[node] = nextN;
}
void updateRangeTree(int qL, int qR, int rL, int rR, int i, int add) {
  if (qL == rL && qR == rR) {
    rt[i].max += add;
    rt[i].lazyAdd += add;
    return;
  }
  int rM = (rL + rR) >> 1;
  int childL = (i << 1) + 1;
  int childR = childL + 1;
  if (rt[i].lazyAdd != 0) {
    rt[childL].max += rt[i].lazyAdd;
    rt[childR].max += rt[i].lazyAdd;
    rt[childL].lazyAdd += rt[i].lazyAdd;
    rt[childR].lazyAdd += rt[i].lazyAdd;
    rt[i].lazyAdd = 0;
  }
  if (qL < rM) updateRangeTree(qL, min(qR, rM), rL, rM, childL, add);
  if (qR > rM) updateRangeTree(max(qL, rM), qR, rM, rR, childR, add);
  rt[i].max = max(rt[childL].max, rt[childR].max);
}
int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(NULL);
  cout.tie(NULL);
  cin >> n >> k;
  for (int i = 0; i < n; i++) {
    cin >> sequence[i];
  }
  edges.resize(n);
  for (int i = n - 1; i >= 0; i--) {
    int nextIndex = i + 1;
    dpNext[i] = n;
    while (nextIndex != n) {
      if (sequence[i] < sequence[nextIndex]) {
        dpNext[i] = nextIndex;
        edges[nextIndex].push_back(i);
        break;
      } else {
        nextIndex = dpNext[nextIndex];
      }
    }
    if (dpNext[i] == n) {
      rootIndices.push_back(i);
    }
  }
  for (int r : rootIndices) {
    topologicalSort(r);
  }
  edges.clear();
  rt.assign(1000000 << 2, {0, 0});
  for (int i = 0; i < k; i++) {
    updateRangeTree(rangeStarts[i], rangeEnds[i], 0, n, 0, 1);
  }
  cout << rt[0].max << " ";
  for (int i = k; i < n; i++) {
    updateRangeTree(rangeStarts[i], rangeEnds[i], 0, n, 0, 1);
    updateRangeTree(rangeStarts[i - k], rangeEnds[i - k], 0, n, 0, -1);
    cout << rt[0].max << " ";
  }
  cout << '\n';
  return 0;
}
