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F - Erase and Rotate

Score : $500$ points

Problem Statement

You are given a sequence $P = (p_1,p_2,\ldots,p_N)$ that contains $1,2,\ldots,N$ exactly once each.
You may perform the following operations between $0$ and $K$ times in total in any order:

• Choose one term of $P$ and remove it.
• Move the last term of $P$ to the head.

Find the lexicographically smallest $P$ that can be obtained as a result of the operations.

Constraints

• $1 \leq N \leq 2 \times 10^5$
• $0 \leq K \leq N-1$
• $1 \leq p_i \leq N$
• $(p_1,p_2,\ldots,p_N)$ contains $1,2,\ldots,N$ exactly once each.
• All values in input are integers.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$p_1$ $p_2$ $\ldots$ $p_N$

Output

Print the lexicographically smallest $P$ that can be obtained as a result of the operations, separated by spaces.

5 3
4 5 2 3 1

1 2 3

The following operations make $P$ equal $(1,2,3)$.

• Removing the first term makes $P$ equal $(5,2,3,1)$.
• Moving the last term to the head makes $P$ equal $(1,5,2,3)$.
• Removing the second term makes $P$ equal $(1,2,3)$.

There is no way to obtain $P$ lexicographically smaller than $(1,2,3)$, so this is the answer.

3 0
3 2 1

3 2 1

You may be unable to perform operations.

15 10
12 10 7 2 8 11 9 1 6 14 3 15 13 5 4

1 3 4 7 2 8 11 9