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 <vector>
#include <algorithm>
#include <iostream>
using namespace std;
int main() {
    int n, k; cin >> n >> k;
    string s; cin >> s;
    char c = *min_element(s.begin(), s.end());
    if (k > 15) {
        cout << string(n, c) << endl;
        return 0;
    }
    s += s;
    reverse(s.begin() + n, s.end());

    vector<int> ps;
    int len = 1;
    for (int i = 0; i < n; ) {
        i = s.find(c, i);
        if (i == string::npos || i > n) break;
        int j = s.find_first_not_of(c, i);
        if (j == string::npos) j = 2*n - i;
        if (j - i > len) {
            len = j - i;
            ps.clear();
            ps.push_back(i);
        } else if (j - i == len) {
            ps.push_back(i);
        }
        i = j;
    }

    if (int rest = n - (len << (k-1)); rest <= 0) {
        cout << string(n, c) << endl;
    } else {
        int ansp = -1;
        for (int p : ps) {
            if (ansp == -1 || s.compare(p + len, rest, s, ansp + len, rest) < 0) ansp = p;
        }
        cout << string(n - rest, c) << s.substr(ansp + len, rest) << endl;
    }
}
