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 MAXN = 5e05 + 10;
int N, K;
int a[MAXN], mapp[MAXN];
int getnum() {
  int num = 0;
  char ch = getchar();
  while (!isdigit(ch)) ch = getchar();
  while (isdigit(ch)) num = (num << 3) + (num << 1) + ch - '0', ch = getchar();
  return num;
}
int main() {
  N = getnum(), K = getnum();
  for (int i = 1; i <= N; i++) a[i] = getnum(), mapp[a[i]] = i;
  for (int i = N - 1; i >= 1; i--) {
    int p = i, stan = mapp[i];
    while (p < N && mapp[p + 1] < stan && stan - mapp[p + 1] >= K)
      p++, swap(mapp[p - 1], mapp[p]);
  }
  for (int i = 1; i <= N; i++) a[mapp[i]] = i;
  for (int i = 1; i <= N; i++) printf("%d\n", a[i]);
  return 0;
}
