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 = 500005;
int a[maxn], pos[maxn], n, k;
inline void read(int &x) {
  x = 0;
  int p = 1;
  char c = getchar();
  while (!isdigit(c)) {
    if (c == '-') p = -1;
    c = getchar();
  }
  while (isdigit(c)) {
    x = (x << 1) + (x << 3) + (c ^ '0');
    c = getchar();
  }
  x *= p;
}
int main() {
  read(n);
  read(k);
  for (register int i = 1; i <= n; ++i) {
    read(a[i]);
    pos[a[i]] = i;
  }
  while (1) {
    if (clock() * 1.0 / CLOCKS_PER_SEC > 1.6) break;
    for (register int i = 1; i <= n; ++i) {
      for (register int j = a[i] - 1; j >= 1; --j) {
        if (pos[j] - i < k) break;
        int tmp = pos[j];
        pos[a[i]] = tmp;
        pos[j] = i;
        swap(a[i], a[tmp]);
      }
    }
  }
  for (register int i = 1; i <= n; ++i) printf("%d\n", a[i]);
  return 0;
}
