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
/*input
10 2
bbaabbbaab

*/

#include <iostream>
#include <algorithm>

using namespace std;

int main()
{
	ios_base::sync_with_stdio(0); cin.tie(0);
	int N, K;
	string S;
	cin >> N >> K >> S;
	S += S;
	reverse(S.begin() + N, S.begin() + 2 * N);

	int idx = 0;
	for (int i = 1; i <= N; ++i) {
		for (int j = 0; j < N; ++j) {
			if (S[idx + j] < S[i + j]) break;
			if (S[idx + j] > S[i + j]) {
				idx = i;
				break;
			}
		}
	}

	int idx2 = idx;
	for (; idx2 < idx + N && S[idx] == S[idx2]; ++idx2);

	--K;
	int part1 = ((N / (idx2 - idx)) >> K) ? ((idx2 - idx) << K) : N;
	for (int i = 0; i < part1; ++i) putchar(S[idx]);
	for (int i = part1; i < N; ++i) putchar(S[idx2 + (i - part1)]);
	putchar('\n');
}