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>
using namespace std;
const int N=10010;
char s[N],ans[N];
int n,k;
int check(int l){
	for (int i=0;i<n;i++){
		if (s[i+l]!=ans[i]){
			return s[i+l]<ans[i];
		}
	}
	return 0;
}
void cov(int l){
	for (int i=0;i<n;i++)
		ans[i]=s[i+l];
}
int main(){
	cin>>n>>k;
	scanf("%s",s);
	for (int i=n;i<2*n;i++)s[i]=s[2*n-1-i];
	cov(0);
	for (int i=1;i<n;i++)
		if (check(i))cov(i);
	int cnt=0,cnt1=0;
	for (int i=0;i<n;i++){
		if (ans[i]!=ans[0])break;
		else cnt++;
	}cnt1=cnt;
	while (k>1&&cnt<n)k--,cnt<<=1;
	cnt=min(cnt,n);
	for (int i=1;i<=cnt;i++)
		putchar(ans[0]);
	for (int i=0;i<n-cnt;i++)
		putchar(ans[i+cnt1]);
	cout<<endl;
}