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>

#define rep(i, n) for (int i = 0; i < (n); i++)
#define repr(i, n) for (int i = (n) - 1; i >= 0; i--)

using namespace std;

int main() {
  cin.tie(nullptr); ios::sync_with_stdio(false);
  int N, K; cin >> N >> K;
  string S; cin >> S;
  char x = *min_element(S.begin(), S.end());
  string ans = "~";
  K = min(K, 30);
  rep(i, N+1) {
    string U = S + string(S.rbegin(), S.rend());
    U = U.substr(i, N);
    rep(_, K-2) {
      int k = 0;
      while (k < N && U.rbegin()[k] == x) k++;
      U = U + string(U.rbegin(), U.rend());
      U = U.substr(k, N);
    }
    if (K >= 2) {
      int k = 0;
      while (k < N && U.rbegin()[k] == x) k++;
      U = U + string(U.rbegin(), U.rend());
      U = U.substr(N - k, N);
    }
    ans = min(ans, U);
  }
  cout << ans << endl;
}