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
import sys

N,K=map(int,input().split())
S=list(input())
MIN=min(S)

def minimum(S):
    T=S+S[::-1]

    ANS=[]

    for i in range(N+1):
        ANS.append(T[i:i+N])

    return min(ANS)

def next(S):
    T=S+S[::-1]
    LIST=[]
    CL=[0]*2*N
    count=0

    for i in range(2*N):
        if T[i]==MIN:
            count+=1

        else:
            count=0

        CL[i]=count

    MAX=max(CL)
    LIST=[]

    for i in range(N-1,2*N):
        if CL[i]==MAX:
            LIST.append(T[i+1-N:i+1])

    return LIST,MAX

def next2(S,x):
    return [MIN]*x+S[x:][::-1]

if K==1:
    print("".join(minimum(S)))

else:
    CAN,MAX=next(S)

    if (MAX<<(K-1))>=N:
        print(MIN*N)
        sys.exit()

    ANS=[]

    for c in CAN:

        ANS.append(next2(c,MAX*((1<<(K-1))-1)))

    print("".join(min(ANS)))