Problem:
Score : 2000 points

Problem Statement

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.

Sample Input 1

4 2
4 2 3 1

Sample Output 1

2
1
4
3

One possible way to obtain the lexicographically smallest permutation is shown below:

4 2 3 1

4 1 3 2

3 1 4 2

2 1 4 3

Sample Input 2

5 1
5 4 3 2 1

Sample Output 2

1
2
3
4
5

Sample Input 3

8 3
4 5 7 8 3 1 2 6

Sample Output 3

1
2
6
7
5
3
4
8

Solution in C (GCC 5.4.1) (judge verdict: Time Limit Exceeded)

#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 + k)){
      if(minsoat[nowmax - 2] - minsoat[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;
}