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() {
    cin >> n >> k;
    cin >> s;

    string t = s;
    reverse(t.begin(), t.end());

    s += t;

    string ans;
    ans.append(n, 'z');
    for(int i=0; i<=n; i++) {
        t = s.substr(i, n);
        ans = min(ans, t);
    }

    int cnt = 0;
    for(int i=0; i<ans.size(); i++) {
        if(ans[i] == ans[0]) cnt++;
        else break;
    }
    int st = cnt;

    for(int i=1; i<k; i++) {
        cnt *= 2;
        if(cnt > n) break;
    }

    for(int i=0; i<cnt && i < n; i++) {
        cout << ans[0];
    }

    for(int i = st; i - st + cnt < n; i++)
        cout << ans[i];
}
