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>
const int N = 500500;
const long long mod = 1e9 + 7;
using namespace std;
int n;
int k;
int a[N];
int main() {
  ios_base::sync_with_stdio(0);
  cin >> n >> k;
  for (int i = 1; i <= n; i++) {
    int x;
    cin >> x;
    a[x] = i;
  }
  if (n > 10000) {
    exit(0);
  }
  while (true) {
    bool did = false;
    for (int i = n - 1; i >= 1; i--) {
      if (a[i] - a[i + 1] >= k) {
        swap(a[i], a[i + 1]);
        did = true;
      }
    }
    if (!did) {
      break;
    }
  }
  vector<int> res(n);
  for (int i = 1; i <= n; i++) {
    res[a[i] - 1] = i;
  }
  for (int x : res) {
    cout << x << "\n";
  }
}
