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 <iostream>
#include <string>
#include <algorithm>
#include <vector>
#include <iomanip>
#include <cmath>
#include <stdio.h>
#include <queue>
#include <deque>
#include <cstdio>
#include <set>
#include <map>
#include <bitset>
#include <stack>
#include <cctype>
using namespace std;
int main() {
   
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    string ans;
    for (int i = 0; i < k; i++) {
        string s1 = ans;
        string s2 = s;
        reverse(s.begin(), s.end());
        s2 += s;
        string s3 = s2;
        reverse(s3.begin(), s3.end());
        vector<string> vec, vec1;
        for (int i = 0; i <= n; i++) {
            vec.emplace_back(s2.substr(i, n));
        }
        for (int i = 0; i <= n; i++) {
            vec1.emplace_back(s3.substr(i, n));
        }
        sort(vec.begin(), vec.end());
        sort(vec1.begin(), vec1.end());
        ans = vec[0];
        if (ans == s1) {
            cout << s << endl;
            return 0;
        }
        s = vec1[0];
        reverse(s.begin(), s.end());
    }
    cout << ans << endl;
    return 0;
}
