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 MAXN = 500005;
int N, K, A[MAXN];
int pos[MAXN];
int stk[MAXN], tp;
int main() {
  scanf("%d%d", &N, &K);
  for (int i = 1; i <= N; i++) scanf("%d", &A[i]), pos[A[i]] = i;
  {
    for (int i = 1; i <= N; i++)
      for (int j = i; j > 1 && pos[j - 1] - pos[j] >= K; j--)
        swap(pos[j], pos[j - 1]);
    for (int i = 1; i <= N; i++) A[pos[i]] = i;
    for (int i = 1; i <= N; i++) printf("%d\n", A[i]);
  }
  {}
  fclose(stdin);
  fclose(stdout);
  return 0;
}
