Score : $1300$ points

Problem Statement

Takahashi has a string $S$ of length $N$ consisting of lowercase English letters. On this string, he will perform the following operation $K$ times:

• Let $T$ be the string obtained by reversing $S$, and $U$ be the string obtained by concatenating $S$ and $T$ in this order.
• Let $S'$ be some contiguous substring of $U$ with length $N$, and replace $S$ with $S'$.

Among the strings that can be the string $S$ after the $K$ operations, find the lexicographically smallest possible one.

Constraints

• $1 \leq N \leq 5000$
• $1 \leq K \leq 10^9$
• $|S|=N$
• $S$ consists of lowercase English letters.

Input

Input is given from Standard Input in the following format:

$N$ $K$

$S$

Output

Print the lexicographically smallest possible string that can be the string $S$ after the $K$ operations.

5 1
bacba

aabca

When $S=$bacba, $T=$abcab, $U=$bacbaabcab, and the optimal choice of $S'$ is $S'=$aabca.

10 2
bbaabbbaab

aaaabbaabb