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 <string>
#include <random>
#include <cassert>
#include <cstring>
#include <chrono>

using namespace std;

typedef long long ll;

string ProcessOnce(string s, bool last) {
  int n = s.size();
  int i = n - 1;
  while (i - 1 >= 0 && s[i - 1] == s[i]) i--;
  string w = s;
  reverse(w.begin(), w.end());
  s += w;
  if (last) return s.substr(i, n);

  int diff = n - 1 - i;
  int right = n + diff;
  int left = right - n + 1;
  return s.substr(left, n);
}

string Process(string s, int k) {
  for (int i = 0 ; i < k; ++i) {
    s = ProcessOnce(s, i == k - 1);
  }
  return s;
}

int main()
{
  int n, k;
  cin >> n >> k;
  string s;
  cin >> s;

  if (k > 20) {
    k = 20;
  }

  string result = "";
  
  string w = s;
  reverse(w.begin(), w.end());

  string ss = s + w;

  for (int i = 0; i <= n; ++i) {
    string cur = ss.substr(i, n);
    cur = Process(cur, k - 1);
    if (result == "" || result > cur) {
      result = cur;
    }
  }
  cout << result << endl;

  return 0;
}
