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;

#define sz(x) ((int) ((x).size()))
typedef long long ll;
typedef long double ld;

int n, k;
string s, sr;

int main() {
  ios_base::sync_with_stdio(false);
  cin.tie(0);
  cout << fixed << setprecision(10);
  cin >> n >> k >> s;
  sr = s;
  reverse(sr.begin(), sr.end());
  vector<string> v;
  for (int i = 0; i < n; i++) {
    string h = s.substr(i, n - i) + sr.substr(0, i);
    v.push_back(h);
  }
  sort(v.begin(), v.end());
  string r = v[0];
  k = min(k - 1, 15);
  for (int i = 0; i < k; i++) {
    int j = 0;
    while (j < n - 1 && r[j + 1] == r[j])
      j++;
    r = r.substr(0, j + 1) + r;
    r = r.substr(0, n);
  }
  cout << r << "\n";
}
