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()
d=s+s[::-1]
d=d[::-1]
r=d[:n]
e=d[:n]
for i in range(n):
    e=e[1:]+d[n+i]
    r=min(r,e)
t=1
qo=r[0]
for i in range(1,n):
    if qo==r[i]:
        t+=1
    else:
        break
r=r[::-1]
for i in range(k-1):
    p=r+r[n-t:]
    p=p[::-1]
    p=p[:n]
    if r==p:
        break
    else:
        r=p[::-1]
        t+=t
print(r[::-1])