Reversing and Concatenating

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.

Examples

Input

5 1 bacba

Output

aabca

Input

10 2 bbaabbbaab

Output

aaaabbaabb

inputFormat

Input

Input is given from Standard Input in the following format:

N K S

outputFormat

Output

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

Examples

Input

5 1 bacba

Output

aabca

Input

10 2 bbaabbbaab

Output

aaaabbaabb

样例

5 1
bacba

aabca