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 $i,j (1 \leq i < j \leq N)$, such that $j - i \geq K$ 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

• $2 \leq N \leq 500,000$
• $1 \leq K \leq N-1$
• $P$ 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.

4 2
4 2 3 1

2
1
4
3

One possible way to obtain the lexicographically smallest permutation is shown below:

• $4 2 3 1$
• $4 1 3 2$
• $3 1 4 2$
• $2 1 4 3$

5 1
5 4 3 2 1

1
2
3
4
5

8 3
4 5 7 8 3 1 2 6

1
2
6
7
5
3
4
8