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=list(input())
l=0
c=0
for i in range(n):
    if s[i]==min(s):
        c+=1
        l=max(l,c)
    else:
        c=0
import sys
input=sys.stdin.readline
s.reverse()
if (2**(k-1))*l>n:
    print(min(s)*n)
else:
    for i in range(min(k,13)):
        t=list(reversed(s))
        u=t+s
        uu=u[:n]
        for j in range(1,n+1):
            x=u[j:j+n]
            if uu>x:
                uu=x
        s=uu
    print("".join(s))
