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>

const int MAXN = 5010;
typedef std::string str;
typedef long long LL;
str get(str buf, int K) {
	// std::cout << "QRY " << buf << ' ' << K << std::endl;
	int L = buf.size(), at = L - 1;
	while (~at && buf[at] == buf[L - 1]) --at;
	int cnt = std::min((LL) (L - at - 1) << K, (LL) L);
	return str(cnt, buf[L - 1]) + str(buf.rbegin() + L - at - 1, buf.rbegin() + L - at + L - cnt - 1);
}
int main() {
	std::ios_base::sync_with_stdio(false), std::cin.tie(0);
	str t, ans; int N, K;
	std::cin >> N >> K >> t; ans = t;
	if (K > 20) ans = std::string(N, *std::min_element(t.begin(), t.end()));
	t = t + str(t.rbegin(), t.rend());
	// std::cout << t << std::endl;
	for (int i = 0; i <= N; ++i) {
		str res = get(t.substr(i, N), K - 1);
		// std::cout << res << std::endl;
		if (res < ans) ans = res;
	}
	std::cout << ans << std::endl;
	return 0;
}
