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 A[500005];
int pos[500005];
int n, K;
void swap_place(int s, int t) {
  swap(pos[A[s]], pos[A[t]]);
  swap(A[s], A[t]);
}
int main() {
  scanf("%d %d", &n, &K);
  for (int i = 0; i < n; i++) {
    scanf("%d", &A[i]);
    A[i]--;
    pos[A[i]] = i;
  }
  for (int i = 0; i + 1 < n; i++) {
    if (pos[i + 1] + K <= pos[i]) {
      swap_place(pos[i + 1], pos[i]);
    }
  }
  for (int i = 0; i < n; i++) {
    while (A[i] > 0) {
      int to = pos[A[i] - 1];
      if (i + K > to) {
        if (A[i] == 1 || to < i) break;
        int to2 = pos[A[i] - 2];
        if (to + K <= to2) {
          swap_place(to, to2);
          swap_place(i, to2);
        } else
          break;
      } else
        swap_place(i, to);
    }
  }
  for (int i = 0; i < n; i++) printf("%d\n", A[i] + 1);
  return 0;
}
