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 n, k;
string s;
int main() {
  cin >> n >> k >> s;
  char c = *min_element(s.begin(), s.end());
  string t = s;
  reverse(t.begin(), t.end());
  s += t;
  int l = 0;
  for (int i = 0, j = 0; i < n << 1; i++) {
    j = s[i] == c ? j + 1 : 0;
    l = max(l, j);
  }
  int l1 = l;
  for (int i = 1; i < k; i++) {
    l <<= 1;
    if (l >= n) {
      for (int i = 0; i < n; i++) putchar(c);
      return 0;
    }
  }
  string x = "{";
  for (int i = 0, j = 0; i < n << 1; i++) {
    j = s[i] == c ? j + 1 : 0;
    if (j == l1) {
      if (i - n < 0) continue;
      string t = s.substr(i - j - n + l + 1 , n - l);
      reverse(t.begin(), t.end());
      x = min(x, t);
    }
  }
  for (int i = 0; i < l; i++) putchar(c);
  cout << x;
}
