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<stdio.h>
#define swap(x,y) do {int a = x;x = y;y = a;} while(0)
int main (){
  int N,K;
  scanf("%d %d",&N,&K);
  int P[N];
  for(int i = 0;i < N;i ++){
    scanf("%d",&P[i]);
  }
  int nowmax = N;
  int minsoat[N];
  for(int i = 0;i < N;i ++){
    for(int j = 0;j < N;j ++){
      if(i + 1 == P[j]){
        minsoat[i] = j;
        j = N;
      }
    }
  }
  for(int k = 0;k < N;k ++){
    while(nowmax > 1){
      if([nowmax - 2] - [nowmax - 1] >= K){
        swap(P[minsoat[nowmax - 2]],P[minsoat[nowmax - 1]]);
        swap(minsoat[nowmax -2],minsoat[nowmax-1]);
      }
      nowmax = nowmax - 1;
    }
    nowmax = N;
  }
  for(int i = 0;i < N;i ++){
    printf("%d\n",P[i]);
  }
  return 0;
}
