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;
  std::cin >> N >> K;
  int P[N];
  for (int i = 0; i < N; ++i) std::cin >> P[i];
  while (true) {
    int count = 0;
    for (int i = 0; i < N; ++i) {
      for (int j = i + K; j < N; ++j) {
        if (P[i] - P[j] == 1) {
          int tmp = P[i];
          P[i] = P[j];
          P[j] = tmp;
          ++count;
          break;
        }
      }
    }
    if (count == 0) break;
  }
  for (int i = 0; i < N; ++i) std::cout << P[i] << std::endl;
  return 0;
}
