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;
typedef long long ll;

int main() {
  ios::sync_with_stdio(0); cin.tie(0);
  int n, k;
  string s;
  cin >> n >> k >> s;
  string t = s;
  reverse(t.begin(), t.end());
  string mi = s;
  s += t;
  for (int i = 0; i < n; i++) {
    mi = min(mi, s.substr(i,n));
  }
  k--;
  while (k--) {
    char c = mi[0];
    int cs = 0;
    while (cs < n && mi[cs] == c) cs++;
    if (cs == n) break;
    mi = (mi.substr(0,cs)+mi).substr(0,n);
  }
  cout << mi << endl;
}
