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;
int N;
char Min='z',Max='a';char ans[200005];
void Check(char *s,int K){
	int now=N,Len=0;
	while (now>=1&&s[now]==Min) Len++,now--;
	if (!Len) exit(0);
	while (K&&Len<N) Len*=2,K--;
	if (Len>=N){
		for (int i=1;i<=N;i++)
			ans[i]=Min;
		cout<<ans+1;
		exit(0);
	}
	static char tmp[100005];
	for (int i=1;i<=Len;i++)
		tmp[i]=Min;
	for (int i=Len+1;i<=N;i++)
		tmp[i]=s[now--];
	for (int i=1;i<=N;i++){
		if (tmp[i]<ans[i]){
			for (int j=1;j<=N;j++)
				ans[j]=tmp[j];
			return;
		}
		else if (tmp[i]>ans[i]) return;
	}
}
int K;
char s[200005];
int main(){
	scanf("%d%d",&N,&K);
	cin>>s+1;
	Min='z';
	Max='a';
	for (int i=1;i<=N;i++){
		Min=min(s[i],Min);
		Max=max(s[i],Max);
		s[2*N-i+1]=s[i];
		ans[i]='z';
	}
	if (Min==Max){
		cout<<s;
		return 0;
	}
	if (s[N]==Min) Check(s,K);
	for (int i=N;i<=2*N;i++)
		if (s[i]==Min) Check(s+i-N,K-1);
	cout<<ans+1;
}