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;
typedef long long ll;

signed main(){
    //cout << setprecision(16) ;
    ios::sync_with_stdio(false);
	cin.tie(0);

    int n,k;
    cin>>n>>k;

    k = min(k,15);

    string s;
    cin>>s;

    char c='z';
    for(int i=0;i<n;i++) c = min(c,s[i]);
    reverse(s.begin(),s.end());

    while(k--){
        string rev = s;
        reverse(rev.begin(),rev.end());
        s = rev + s;
        vector<string> v;
        //cerr<<s<<endl;
        if(k){
            for(int i=n-1;i<n*2;i++){
                if(s[i] == c){
                    string t = s.substr(i-n+1, n);
                    reverse(t.begin(),t.end());
                    v.push_back(t);
                }
            }
            sort(v.begin(),v.end());
            s=v[0];
        }
        else{
            for(int i=0;i<=n;i++){
                if(s[i] == c){
                    string t = s.substr(i, n); 
                    v.push_back(t);
                    //cerr<<t<<endl;
                }
            }
            sort(v.begin(),v.end());
            s = v[0];
        }
    }
    cout<<s<<endl;

}