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: Wrong Answer)

#include<stdio.h>

int main()
{
    int N,K;
    scanf("%d",&N);
    scanf("%d",&K);
    int P[N];
    for(int i=0; i<N; i++)
    {
        scanf("%d",&P[i]);
    }
    int i=0,j;
    while(i!=(N-K))
    {
        j = i+K;
        while(j!=N)
        {
            if(P[i]-P[j]==1)
            {
                int temp;
                temp = P[i];
                P[i] = P[j];
                P[j] = temp;
            }
            j++;
        }
        i++;
        if(i==(N-K))
        {
            for(int a=K ; a<N; a++)
            {
                if(P[0]>P[a])
                {
                    i=0;
                    break;
                }
            }
        }
    }
    for(i=0; i<N; i++)
    {
        printf("%d\n",P[i]);
    }
    return 0;
}