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
N, K = [int(x) for x in input().split()]
nums = [int(x) for x in input().split()]

def f_swap(nums, N, K):
  for i in range(0, N-K):
    for j in range(i+K, N):
      if nums[i] - nums[j] == 1:
        nums[i], nums[j] = nums[j], nums[i]
        return 1
  return 0

while True:
  if not f_swap(nums, N, K):
    break

for n in nums:
  print(n)
  