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 MIN_INT -2147483648
#define MAX_INT 2147483647
#define MIN_LONG -9223372036854775808L
#define MAX_LONG 9223372036854775807L

#define long long long int

using namespace std;

// @author: pashka

int main() {
    ios::sync_with_stdio(false);

    int n, k;
    cin >> n >> k;
    k = min(k, 15);
    string s;
    cin >> s;
    string t = s;
    reverse(t.begin(), t.end());
    string u = s + t;
    string res = s;
    for (int i = 0; i + n <= u.size(); i++) {
        string ss = u.substr(i, n);
        if (k > 0) {
            int j = n - 1;
            while (j >= 0 && ss[j - 1] == ss[n - 1]) j--;
            int x = min((n - j) << (k - 1), n);
            string s3 = "";
            for (int t = 0; t < x; t++) s3 += ss[n - 1];
            for (int t = 0; t < n - x; t++) {
                s3 += ss[j - 1 - t];
            }
            ss = s3;
        }
        if (ss < res) {
            res = ss;
        }
    }
    cout << res;
    
    return 0;
}