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()
T = S[::-1] #文字列反転
U = S + T
D = []
for i in range(N):
  D.append(U[i:i+N])
D.sort()
B = D[0]
for i in range(N):
  if B[i] != B[0]:
    break
if i * 1 << (K - 1) > N:
  print(B[0] * N)
else:
  print((B[0] * (i * (1 << (K - 1))) + B[i:])[:N])