You are given a permutation P_1 ... P_N of the set {1, 2, ..., N}.

You can apply the following operation to this permutation, any number of times (possibly zero):

* Choose two indices i,j (1 ≦ i < j ≦ N), such that j - i ≧ K and |P_i - P_j| = 1. Then, swap the values of P_i and P_j.



Among all permutations that can be obtained by applying this operation to the given permutation, find the lexicographically smallest one.

Constraints

* 2≦N≦500,000
* 1≦K≦N-1
* P is a permutation of the set {1, 2, ..., N}.

Input

The input is given from Standard Input in the following format:


N K
P_1 P_2 ... P_N


Output

Print the lexicographically smallest permutation that can be obtained.

Examples

Input

4 2
4 2 3 1


Output

2
1
4
3


Input

5 1
5 4 3 2 1


Output

1
2
3
4
5


Input

8 3
4 5 7 8 3 1 2 6


Output

1
2
6
7
5
3
4
8
#include <bits/stdc++.h>
using namespace std;
const int N = 2e3 + 123;
const long long mod = 1e9 + 7;
int n, cnt[N], a[N], k, ans[N];
vector<int> g[N];
int main() {
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    cin >> a[i];
  }
  for (int i = 1; i <= n; i++) {
    for (int j = 1; j <= n; j++) {
      if (a[i] < a[j] && abs(i - j) < k) {
        cnt[i]++;
        g[j].push_back(i);
      }
    }
  }
  for (int i = n; i >= 1; i--) {
    for (int j = n; j >= 1; j--) {
      if (cnt[j] == 0) {
        ans[i] = j;
        for (int u : g[j]) {
          cnt[u]--;
        }
        cnt[j] = N;
        break;
      }
    }
  }
  for (int i = 1; i <= n; i++) cout << ans[i] << "\n";
}
