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
N,K = map(int,input().split())
S = input()


if N < 2**K:
    S_young = sorted(list(S))[0]
    print(S_young*N)
    
else:
    word=S
    S=S+S[::-1]
    for i in range(K):
        for j in range(N-1):
            if word > S[1+j:1+j+N]:
                word = S[1+j:1+j+N]
        S = word[::-1]+word
    print(word)