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 <algorithm>
#include <string>

void solve() {
    int n, k;
    std::string s;
    std::cin >> n >> k >> s;

    std::string u = s;
    std::reverse(u.begin(), u.end());
    u = s + u;

    int si = 0;
    for (int i = 1; i < n; ++i) {
        if (u.substr(i, n) < u.substr(si, n)) si = i;
    }
    u = u.substr(si, n);

    int l;
    for (l = 0; l < n; ++l) {
        if (u[l] != u[0]) break;
    }
    auto back = u.substr(l);

    --k;
    while (l < n && k > 0) {
        l = std::min(n, l * 2);
        --k;
    }

    auto ans = std::string(l, u[0]) + back;
    ans = ans.substr(0, n);
    std::cout << ans << std::endl;
}

int main() {
    std::cin.tie(nullptr);
    std::cout.tie(nullptr);
    std::ios::sync_with_stdio(false);

    solve();

    return 0;
}
