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;
int read() {
  int x = 0, f = 1, ch = getchar();
  while (ch > '9' || ch < '0') {
    if (ch == '-') f = -1;
    ch = getchar();
  }
  while (ch >= '0' && ch <= '9') {
    x = x * 10 + ch - '0';
    ch = getchar();
  }
  return x * f;
}
const int MAXN = 500000 + 10;
int p[MAXN], a[MAXN];
int main() {
  int n = read(), k = read();
  ;
  for (register int i = 1; i <= n; i++) p[i] = read(), a[p[i]] = i;
  while (1) {
    bool flag = 0;
    for (register int i = n; i >= 1; i--)
      if (a[i - 1] - a[i] >= k)
        swap(p[a[i]], p[a[i - 1]]), swap(a[i], a[i - 1]), flag = 1;
    if (!flag) break;
  }
  for (register int i = 1; i <= n; i++) printf("%d\n", p[i]);
  return 0;
}
