Problem:
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

Solution in PyPy3 (2.4.0) (judge verdict: Accepted)

N, K = map(int, input().split())
S = input()
SS = S + S[::-1]
D = []
for i in range(N):
  D.append(SS[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])