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 MN = 500010;
int N, K;
int P[MN], Q[MN];
int main() {
  scanf("%d %d", &N, &K);
  for (int i = 0; i < (N); i++) {
    scanf("%d", &P[i]);
    --P[i];
    Q[P[i]] = i;
  }
  if (N > 2000) return 0;
  vector<int> res(N), ans(N);
  vector<int> us(N);
  int now = 0;
  for (int tt = 0; tt < (N); tt++) {
    set<int> st;
    int c = N;
    for (int i = 0; i < (N); i++)
      if (!us[Q[i]]) {
        auto it = st.upper_bound(Q[i] - K);
        if (!(it != st.end() && *it < Q[i] + K)) {
          c = min(c, Q[i]);
        }
        st.insert(Q[i]);
      }
    if (c != N) {
      res[now++] = c;
      us[c] = 1;
    }
  }
  for (int i = 0; i < (N); i++) ans[res[i]] = i;
  for (int i = 0; i < (N); i++) printf("%d\n", ans[i] + 1);
  return 0;
}
