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;

int main() {
    ios::sync_with_stdio(0);
    cin >> n >> k >> s;
    while (k--) {
        string lst = s, u = s;
        reverse(s.begin(), s.end()), u.append(s);
        for (int i = 0; i + n - 1 < u.length(); i++) {
            s = min(s, u.substr(i, s.length()));
        }
        if (k) reverse(s.begin(), s.end());
        if (s == lst) { cout << s << endl; return 0; }
    }
    cout << s << endl;
    return 0;
}