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
#include<bits/stdc++.h>
const int N=5010;
int n,k,l[N*2];
char s[N*2],mc='z';
int cmp(int i,int j){
	for (;s[i]==s[j];i++,j++);
	return s[i]<s[j];
}
int main(){
	scanf("%d%d%s",&n,&k,s);
	for (int i=0;i<n;i++)(s[n*2-i-1]=s[i])<mc?mc=s[i]:1;
	if (k>15)k=15;
	int ml=0;
	for (int i=0;i<n*2;i++){
		l[i+1]=s[i]==mc?l[i]+1:0;
		l[i+1]>ml?ml=l[i+1]:1;
	}
	int r=n-(ml<<k-1);
	if (r<0)r=0;
	int p=-1;
	for (int i=n;i<=n*2;i++)
		if (l[i]==ml&&(p<0||cmp(n*2-i+ml,p)))p=n*2-i+ml;
	for (int i=n-r;i--;)putchar(mc);
	for (int i=0;i<r;i++)putchar(s[p+i]);
	puts("");
}