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 rep(i, n) for (int i = 0; i < n; i++)
using namespace std;
using ll = long long;
using P = pair<int, int>;

string reverse_copy_string(string s) {
    string t;
    int n = s.size();
    for (int i = n-1; i >= 0; i--) {
        t.push_back(s[i]);
    }
    return t;
}

int main() {
    int n, k;
    cin >> n >> k;
    string s, t, u;
    cin >> s;
    t = reverse_copy_string(s);
    u = s + t;
    rep(i,min(14, k)) {
        t = u.substr(0,n);
        rep(j,n-1) {
            if (t > u.substr(j+1,n)) { 
                t = u.substr(j+1,n);
            }
        }
        s = reverse_copy_string(t);
        u = s + t;
    }
    cout << t << endl;
}
