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
import numpy as np

def func():
    line1 = input('')
    line2 = input('')
    line1 = line1.split(' ')
    line2 = line2.split(' ')

    N = int(line1[0])
    K = int(line1[1])
    
    ar = np.zeros([N],np.int)
    for i in range(0,N):
        ar[i] = line2[i]
    flag = True
    while flag:
        flag = False
        for i in range(0,N):
            for j in range(i+K,N):
                if(np.abs(ar[i] - ar[j]) == 1):
                    if(ar[i] > ar[j]):
                        tmp = ar[i]
                        ar[i] = ar[j]
                        ar[j] = tmp
                        flag = True

    for i in range(0,N):
        print(ar[i])

func()
