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.

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.