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 Python (3.4.3) (judge verdict: Wrong Answer)

def E(S, N):
    T = S[::-1]
    U = S+T
    return sorted([U[i:N+i] for i in range(N)])[:10]

N, K = input().split()
N, K = int(N), int(K)
S = [input()]

for i in range(K):
    memory = []
    for s in S:
        memory.append(E(s, N))
    S = sorted([s for i in range(len(memory)) for s in memory[i]])[:10]
print(sorted(S)[0])