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>

#define rep(i,n) for(int i=0;i<(n);i++)

using namespace std;

int main(){
	int n,k;
	string s; cin>>n>>k>>s;

	k=min(k,15);

	rep(i,k-1){
		s=s+s;
		reverse(s.begin()+n,s.end());

		string t="~";
		rep(j,n+1){
			string tmp=s.substr(j,n);
			reverse(tmp.begin(),tmp.end());
			t=min(t,tmp);
		}
		reverse(t.begin(),t.end());
		s=t;
	}

	string ans="~";
	s=s+s;
	reverse(s.begin()+n,s.end());
	rep(j,n+1) ans=min(ans,s.substr(j,n));
	cout<<ans<<'\n';

	return 0;
}
