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]
u="".join([s,t])
ls=[]
for i in range(n):
  ls.append(u[i:i+n])
ls.sort()
k-=1
x=ls[0]
cnt=1
for i in range(1,n):
  if x[0]==x[i]:
    cnt+=1
  else:
    break
if cnt*2**k<n:
  y=n-cnt*2**k
  print(x[0]*(cnt*2**k)+x[cnt:y+cnt])
else:
  print(x[0]*n)
