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,k,mi='z';
string s,ns,ans;
void getans(int l,int r){
	int su=(r-l+1);
	for (int i=1;i<k;i++){
		su=min(su*2,n);if (su==n) break;
	}
	string no="";
	for (int i=1;i<=su;i++) no+=mi;
	for (int i=1;i<=n-su;i++)no+=s[r+i];
	if (ans=="") ans=no;else ans=min(ans,no);
}
int main(){
	cin>>n>>k;
	cin>>s;ns=s;reverse(ns.begin(),ns.end());s+=ns;
	ans="";
	for (int i=0;i<n;i++)mi=min(mi,(int)s[i]);
	for (int i=n-1;i>=0;i--){
		if (s[i]==mi){
			int j=i;
			while (j-1>=0&&s[j-1]==s[i]) j--;
			if (i!=n-1)getans(j,i);else getans(j,n*2-j-1);
		}
	}
	cout<<ans<<endl;
	return 0;
}