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())
k=min(k,20)
S=list(input())
for i in range(n):
  S[i]=ord(S[i])-97
T=S[::-1]
U=S+T
f=0
for i in range(26):
  A=[]
  for j in range(2*n):
    if U[j]==i:
      f=1
      A.append(j)
  if f==1:
    c=i
    break
B=[]
a=1
for i in range(1,len(A)):
  if A[i]==A[i-1]+1:
    a=a+1
    if A[i]>=n:
      B.append([a,A[i]])
  else:
    a=1
    if A[i]>=n:
      B.append([a,A[i]])
C=[]
b=max(B[i][0] for i in range(len(B)))
for i in range(len(B)):
  if B[i][0]==b:
    C.append(B[i][1])
if b*2**(k-1)>=n:
  for i in range(n):
    print(chr(97+c),end="")
  print()
  exit()
Ans=[]
d=n-b*2**(k-1)
for i in range(len(C)):
  AAns=U[C[i]-d-b+1:C[i]-b+1]
  Ans.append(AAns[::-1])
Ans.sort()
for i in range(b*2**(k-1)):
  print(chr(97+c),end="")
for i in range(n-b*2**(k-1)):
  print(chr(97+Ans[0][i]),end="")
print()