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.

Sample Input 1

5 1
bacba

Sample Output 1

aabca

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

Sample Input 2

10 2
bbaabbbaab

Sample Output 2

aaaabbaabb