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 <iostream>
#include <vector>
#include <string>
#include <algorithm>
#include <math.h>
using namespace std;

int main(void){
	int n,k;
	cin>>n>>k;
	string s;
	cin>>s;
	string t = s;
	reverse(t.begin(),t.end());
	s += t;

	vector<string> kouho;
	for(int i=0; i<n; i++){
		kouho.push_back(s.substr(i,n));
	}
	sort(kouho.begin(),kouho.end());

	char a = kouho[0][0];
	string ans = "";
	int i = 0;
	while(ans.size() < n && kouho[0][i] == a){
		for(int j=0; j < pow(2,min(20, k-1)) && ans.size() < n; j++){
			ans.push_back(a);
		}
		i++;
	}
	while(ans.size() < n){
		ans.push_back(kouho[0][i]);
		i++;
	}

	cout<<ans<<endl;

	return 0;
}
