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 INF = 0x3f2f1f0f;
const long long LINF = 1ll * INF * INF;
const int MAX_N = 5e5 + 100;
int N, K, Nr[MAX_N], Ix[MAX_N];
int Ans[MAX_N];
int main() {
  cin >> N >> K;
  for (int i = 0; i < N; i++) {
    scanf("%d", &Ix[i]), Ix[i]--;
    Nr[Ix[i]] = i;
  }
  sort(Nr, Nr + N, [&](int a, int b) {
    if (abs(a - b) < K) return Ix[a] < Ix[b];
    return a < b;
  });
  for (int i = 0; i < N; i++) printf("%d\n", Nr[i] + 1);
  return 0;
}
