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>
int n, K, w[501000], R[501000], top;
int main() {
  int i, j, pv;
  scanf("%d%d", &n, &K);
  if (n > 2000) return 0;
  for (i = 1; i <= n; i++) {
    scanf("%d", &R[i]);
    w[R[i]] = i;
  }
  for (i = 1; i <= n; i++) {
    for (j = i - 1; j >= 1; j--)
      if (w[j] < w[i] + K) break;
    pv = j + 1;
    int x = w[i];
    for (j = i; j > pv; j--) w[j] = w[j - 1];
    w[pv] = x;
  }
  for (i = 1; i <= n; i++) R[w[i]] = i;
  for (i = 1; i <= n; i++) printf("%d\n", R[i]);
}
