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;
int main() {
  int n, k;
  scanf("%d%d", &n, &k);
  vector<int> p(n);
  for (int i = 0; (i) < int(n); ++(i)) scanf("%d", &p[i]);
  vector<int> q(n);
  for (int i = 0; (i) < int(n); ++(i)) q[p[i] - 1] = i;
  for (int i = 0; (i) < int(n); ++(i)) {
    for (int j;;) {
      j = i - 1;
      for (; j >= 0 and q[j] >= q[j + 1] + k; --j) {
        swap(q[j], q[j + 1]);
      }
      if (j == i - 1) break;
    }
  }
  for (int i = 0; (i) < int(n); ++(i)) p[q[i]] = i + 1;
  for (int p_i : p) {
    printf("%d\n", p_i);
  }
  return 0;
}
