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.

Input is given from Standard Input in the following format: >$N$ $K$\ >$S$ #### Constraints - $1 \leq N \leq 5000$ - $1 \leq K \leq 10^9$ - $|S|=N$ - $S$ consists of lowercase English letters.

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

***For Sample #1:*** When $S=$`bacba`, $T=$`abcab`, $U=$`bacbaabcab`, and the optimal choice of $S'$ is $S'=$`aabca`.