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 <algorithm>
#include <iostream>
#include <string>
using namespace std;

int main()
{
    int n, k;
    cin >> n >> k;
    string s;
    cin >> s;
    string t = s;
    reverse(t.begin(), t.end());
    s += t;
    int l = 0;
    for(int i = 1; i <= n; i++){
        if(s.substr(i, n) < s.substr(l, n)) l = i;
    }
    int c, r = 0;
    for(c = 1; c < n; c++){
        if(s[l + c] != s[l]){
            r = l + c;
            break;
        }
    }
    for(int i = 0; i < k - 1; i++){
        c <<= 1;
        if(c >= n){
            c = n;
            break;
        }
    }
    for(int i = 0; i < c; i++) cout << s[l];
    for(int i = 0; i < n - c; i++) cout << s[r + i];
    cout << endl;
}
