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()

lex_min = "z"
for char in S:
  lex_min = min(char, lex_min)

U = S + S[::-1]

L = 0
L_max = 0
for i in range(N << 1):
  if U[i] == lex_min:
    L_max += 1
  else:
    L = max(L, L_max)
    L_max = 0
L = max(L, L_max)

if (1 << (K - 1)) * L >= N:
  print(lex_min * N)
else:
  candidates = []
  n = (1 << (K - 1)) * L
  for i in range(N, N << 1):
    if U[i-L+1:i+1] == L * lex_min:
      cand = n * lex_min + U[i-N+n-L+1:i-L+1][::-1]
      candidates.append(cand)
      
  print(min(candidates))