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<string>
#include<algorithm>
using namespace std;
string s;
int n,k;
int main(){
    cin>>n>>k>>s;
    s+=string(s.rbegin(),s.rend());
    if(k>20)cout<<string(n,*min_element(s.begin(),s.end()))<<'\n';else{
        while(k--){
            string t(s,0,n);
            reverse(t.begin(),t.end());
            for(int i=1;i<=n;++i){
                string p(s,i,n);
                reverse(p.begin(),p.end());
                if(p<t)t=p;
            }
            s=string(t.rbegin(),t.rend())+t;
        }
        s.erase(0,n);
        cout<<s<<'\n';
    }
    return 0;
}