Problem Statement

You are given a permutation $P=(P_1,P_2,\dots,P_N)$ of integers from $1$ to $N$ and an integer $K$.

Consider the following operation on the permutation $P$.

• Choose an integer $i$ such that $1 \leq i \leq N-K+1$, and sort $P_i,P_{i+1},\dots,P_{i+K-1}$ in ascending order. That is, let $(x_1,x_2,\dots,x_K)$ be the result of arranging $P_i,P_{i+1},\dots,P_{i+K-1}$ in order from smallest to largest, and replace $P_{i+j-1}$ with $x_j$ for each $1 \leq j \leq K$.

Find the lexicographically largest permutation that can be obtained by performing the above operation on $P$ exactly once.

What is lexicographical order on sequences? A sequence $S = (S_1,S_2,\ldots,S_{|S|})$ is lexicographically smaller than $T = (T_1,T_2,\ldots,T_{|T|})$ when 1. or 2. below holds. Here, $|S|$ and $|T|$ denotes the lengths of $S$ and $T$, respectively. $|S| \lt |T|$ and $(S_1,S_2,\ldots,S_{|S|}) = (T_1,T_2,\ldots,T_{|S|})$. There is an integer $1 \leq i \leq \min\lbrace |S|, |T| \rbrace$ that satisfy both of the following: $(S_1,S_2,\ldots,S_{i-1}) = (T_1,T_2,\ldots,T_{i-1})$. $S_i$ is smaller than $T_i$ (as a number).

Constraints

• $1 \leq K \leq N \leq 2 \times 10^5$
• $1 \leq P_i \leq N$
• $(P_1,P_2,\dots,P_N)$ is a permutation of integers from $1$ to $N$.
• All input values are integers.

Input

The input is given from Standard Input in the following format:

N K
P_1 P_2 \dots P_N

Output

Print the lexicographically largest permutation that can be obtained by performing the above operation on $P$ exactly once, with spaces in between.