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 <algorithm>
#include <iostream>
#include <algorithm>
using namespace std;

int main(){
  int N, K;
  cin >> N >> K;
  string s;
  cin >> s;
  string ans = s;
  for(int j = 0; j < min(N,K); ++j){
    string t = s;
    reverse(t.begin(), t.end());
    s += t;
    for(int i = 0; i < N; ++i){
      string x = s.substr(i,N);
      //cerr << i << " " << x << endl;
      ans = min(ans,x);
    }
    //cerr << ans << endl;
    reverse(ans.begin(), ans.end());
    s = ans;
    string tmp = s;
    sort(tmp.begin(), tmp.end());
    if(tmp[0] == tmp.back())
      break;
  }
  reverse(ans.begin(), ans.end());
  cout << ans << endl;
}
