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;
int main(){
    int n,k;
    cin >> n >> k;
    string s;
    cin >> s;
    if(k > log2(n)){
        // log2(n)回以上出来るなら全ての文字を辞書順最小のものに出来る
        sort(s.begin(), s.end());
        char x = s[0];
        for(int i=0;i<n;i++) cout << x;
        cout << endl;
    }else{
        //多くて13回程度, シミュレートして間に合う
        string ans = s;
        for(int i=0;i<k;i++){
            string rev = s;
            reverse(rev.begin(), rev.end());
            s += rev;
            if(i!=k-1){
                string nxt = rev;
                reverse(s.begin(), s.end());
                for(int pos = 0; pos < s.size() - n; pos++){
                    nxt = min(nxt, s.substr(pos, n));
                }
                reverse(nxt.begin(), nxt.end());
                s = nxt;
            }else{
                for(int pos = 0; pos < s.size() - n; pos++){
                    ans = min(ans, s.substr(pos, n));
                }
            }
        }
        cout << ans << endl;
    }
}