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
input_word = input()
input_list = input_word.split(" ")
N = int(input_list[0])
K = int(input_list[1])
input_word = input()
tmp_list = input_word.split(" ")
input_list = [ int(i) for i in tmp_list ]

while True:
  flag = 0
  for i in range(1,N):
    number = input_list.index(i)
    number_1 = input_list.index(i+1)
    if number - number_1 >= K:
        input_list[number_1],input_list[number] = input_list[number],input_list[number_1]
        flag = 1
        break
  if flag == 0:
    break

for i in input_list:
  print(i)
      