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<algorithm>
using namespace std;
int N,K;
string s;
int main()
{
	cin>>N>>K>>s;
	string t=s;
	reverse(t.begin(),t.end());
	s+=t;
	string m=s.substr(0,N);
	for(int i=1;i<=N;i++)m=min(m,s.substr(i,N));
	int l=1;
	while(l<m.size()&&m[0]==m[l])l++;
	long k=l;
	K--;
	if(K>17)k=N;
	else k<<=K;
	string ans="";
	while(ans.size()<N&&k>0)k--,ans+=m[0];
	ans+=m.substr(l,N-ans.size());
	cout<<ans<<endl;
}
