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;
#define ri register int
const int N=5e3+5;
string ans;
char s[N<<1];
int main(){
	ri n,k,i,j,x,res;
	scanf("%d%d%s",&n,&k,s+1);
	char c='z';
	for(i=1;i<=n;++i) c=min(c,s[i]),s[2*n-i+1]=s[i];
	if(k>=14){
		while(n--) printf("%c",c);
		return 0;
	}
	for(i=1;i<=n<<1;i=j+1)
		if(s[i]!=c) j=i;
		else{
			for(j=i;j+1<=n<<1&&s[j+1]==c;++j);
			if(j<n) continue;
			res=(j-i+1)*(1<<k-1);
			if(res>=n){
				while(n--) printf("%c",c);
				return 0;
			}
			if(i-1<n-res) continue;
			string now;
			for(x=1;x<=res;++x) now+=c;
			res=n-res;
			for(x=i-1;x>=i-res;--x) now+=s[x];
			ans=ans.empty()?now:min(ans,now);
		}
	cout<<ans<<endl;
    return 0;
}