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 main() {
  int N, K;
  scanf("%d", &N);
  scanf("%d", &K);
  int P[N];
  for (int i = 0; i < N; i++) {
    scanf("%d", &P[i]);
  }
  int i = 0, j;
  while (i != (N - K)) {
    j = i + K;
    while (j != N) {
      if (P[i] - P[j] == 1) {
        int temp;
        temp = P[i];
        P[i] = P[j];
        P[j] = temp;
      }
      j++;
    }
    i++;
    if (i == (N - K)) {
      for (int a = K; a < N; a++) {
        if (P[0] > P[a]) {
          i = 0;
        }
      }
    }
  }
  for (i = 0; i < N; i++) {
    printf("%d\n", P[i]);
  }
}
