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.

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.

Constraints

• 2≦N≦500,000
• 1≦K≦N-1
• P is a permutation of the set {1, 2, ..., N}.

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

见题面 Input 部分

见题面 Output 部分