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;

string singleOperation(string s, int n)
{
  string res = s;
  for (int i = n - 1; i >= 0; i--)
    s += s[i];
  for (int i = 1; i <= n; i++)
    res = min(res, s.substr(i, n));
  return res;
}

string findCandidate(string s, int n)
{
  for (int i = n - 1; i >= 0; i--)
    s += s[i];

  string candidate = "{";
  for (int i = 1; i <= n; i++)
  {
    string u = s.substr(i, n);
    reverse(u.begin(), u.end());
    candidate = min(candidate, u);
  }

  reverse(candidate.begin(), candidate.end());
  return candidate;
}

int main()
{
  int n, k;
  string s;
  cin >> n >> k >> s;
  for (int i = 0; i < min(15, k - 1); i++)
    s = findCandidate(s, n);
  cout << singleOperation(s, n) << endl;
}
