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, t;

string solve();

int main() {
  cin >> n >> k >> s;
  t = s;
  reverse(t.begin(), t.end());
  t = s + t;
  cout << solve() << endl;
  return 0;
}

string solve() {
  string res = s;
  if (k == 1) {
    for (int i = 0; i <= n; ++i) res = min(res, t.substr(i, n));
    return res;
  }
  for (int i = 0; i < n; ++i) {
    int id = i + n, cnt = 0;
    while (id > i && t[i + n] == t[id]) --id, ++cnt;
    for (int j = 1; j < k && cnt < n; ++j) cnt = min(n, cnt * 2);
    string now(cnt, t[i + n]);
    while (now.size() < n) now += t[id--];
    res = min(res, now);
  }
  return res;
}