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 read() {
  int x = 0, l = 1;
  char ch = getchar();
  while (!isdigit(ch)) {
    if (ch == '-') l = -1;
    ch = getchar();
  }
  while (isdigit(ch)) x = x * 10 + (ch ^ 48), ch = getchar();
  return x * l;
}
using namespace std;
int a[500003], wz[500003];
int main() {
  int n = read(), k = read();
  bool fl;
  for (int i = 1; i <= n; i++) a[i] = read(), wz[a[i]] = i;
  do {
    fl = 0;
    for (int i = 1; i <= n - 1; i++)
      if (wz[i] - wz[i + 1] >= k) {
        swap(a[wz[i + 1]], a[wz[i]]);
        swap(wz[i + 1], wz[i]);
        fl = 1;
      }
  } while (fl);
  for (int i = 1; i <= n; i++) printf("%d\n", a[i]);
  return 0;
}
