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, t, mx;

string get_min(string s)
{
    string ans = mx;
    for (int i = 0; i <= n; i++)
        ans = min(ans, s.substr(i, n));
    return ans;
}

int main()
{
    ios_base::sync_with_stdio(false);
    cin.tie(nullptr);
    cin >> n >> k >> s;
    for (int i = 0; i < n; i++)
        mx += 'z';
    k = min(k - 1, 13);
    t = s; reverse(t.begin(), t.end());
    s = get_min(s + t);
    while (k--)
    {
        t = s; reverse(t.begin(), t.end());
        s = get_min(t + s);
    }
    cout << s;
}
