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 N = 1e5 + 1e3 + 7;
int n, k, a[N], pos[N];
void solve1() {
  int tt;
  if (n <= 2000)
    tt = 300000;
  else
    tt = 4500;
  for (int j = 1; j <= tt; j++) {
    for (int i = 1; i < n; i++)
      if (pos[i] - pos[i + 1] >= k)
        swap(a[pos[i]], a[pos[i + 1]]), swap(pos[i], pos[i + 1]);
  }
}
int main() {
  scanf("%d%d", &n, &k);
  if (k == 1) {
    for (int i = 1; i <= n; i++) printf("%d\n", i);
    return 0;
  }
  for (int i = 1; i <= n; i++) scanf("%d", &a[i]), pos[a[i]] = i;
  solve1();
  for (int i = 1; i <= n; i++) printf("%d\n", a[i]);
}
