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 main() {
  int N, K, P[500000];
  cin >> N >> K;
  int pos[500000];
  for (int i = 0; i < N; i++) {
    cin >> P[i];
    --P[i];
    pos[P[i]] = i;
  }
  bool flag = true;
  while (flag) {
    flag = false;
    for (int i = N - 1; i > 0; i--) {
      if (pos[i - 1] - pos[i] >= K) {
        swap(pos[i], pos[i - 1]);
        flag = true;
      }
    }
  }
  vector<int> ans(N);
  for (int i = 0; i < N; i++) ans[pos[i]] = i + 1;
  for (int i = 0; i < N; i++) cout << ans[i] << endl;
}
