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
from math import floor, log
inpl = lambda: list(map(int,input().split()))
N, K = inpl()
S = input()
U = S + S[::-1]
Sp = sorted([ U[i:i+N] for i in range(N+1)])[0]
n = 0
while Sp[n] == Sp[0]:
    n += 1

if K > int(floor(log(N/n)/log(2))) + 1:
    print(Sp[0]*N)
else:
    m = n * (2**(K-1))
    if m >= N:
        print(Sp[0]*N)
    else:
        print(Sp[0]*m + Sp[n:n+N-m])
