Contest Duration: - (local time) (150 minutes) Back to Home
E - Reversing and Concatenating /

Time Limit: 2 sec / Memory Limit: 1024 MB

### 問題文

• S を反転した文字列を T として、ST をこの順に連結して得られる文字列を U とする。
• ある U の連続する長さ N の部分文字列を S' として、SS' で置き換える。

• 1 ≦ N ≦ 5000
• 1 ≦ K ≦ 10^9
• |S|=N
• S は英小文字からなる

### 入力

N K
S


### 入力例 1

5 1
bacba


### 出力例 1

aabca


S=bacbaのとき、T=abcab, U=bacbaabcabであるので S'=aabcaとするのが最適です。

### 入力例 2

10 2
bbaabbbaab


### 出力例 2

aaaabbaabb


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