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 DIM = 5e5 + 5;
int v[DIM], w[DIM];
int main(void) {
  int n, k;
  scanf("%d %d", &n, &k);
  for (int i = 1; i <= n; i++) {
    int x;
    scanf("%d", &x);
    v[x] = i;
  }
  while (true) {
    bool ok = true;
    for (int i = 1; i < n; i++) {
      if (v[i] - v[i + 1] >= k) {
        swap(v[i], v[i + 1]);
        ok = false;
      }
    }
    if (ok) break;
  }
  for (int i = 1; i <= n; i++) w[v[i]] = i;
  for (int i = 1; i <= n; i++) printf("%d\n", w[i]);
  return 0;
}
