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 (3.8.2) (judge verdict: Runtime Error)

n, k = map(int, input().split())
s = input()
rev_s = s + s[::-1]
mido = "z" * n
for i in range(n + 1):
    if mido > rev_s[i:i + n]:
        mido = rev_s[i:i + n]
ind = float("inf")
for i in range(n):
    if mido[i] != mido[0]:
        if i > ind:
            ind = i
ans = ind * (2 ** (k - 1))
print((mido[0] * ans + mido[ind:ind + n - ans])[:n])