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
str = input()
a = str.split(" ")
n = (int)(a[0])
k = (int)(a[1])
str = input()
before = ""
for ii in range(k-1):
  s = str + str[::-1]
  s1 = s[0:n]
  for i in range(1,n+1):
    s2 = s[i:n+i]
    if(s1>s2):
      s1 = s2
  str = s1[::-1]
  if(before==str):
    break
  before = str

s = str + str[::-1]
s1 = s[0:n]
for i in range(1,n+1):
  s2 = s[i:n+i]
  if(s1>s2):
    s1 = s2
print(s1)

